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Tool in homological algebra
algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations. Spectral sequences are a generalization
Spectral_sequence
Classification of stars based on spectral properties
demonstrated that the O-B-A-F-G-K-M spectral sequence is actually a sequence in temperature. Because the classification sequence predates our understanding that
Stellar_classification
Mathematical sequence
In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray. It is usually seen nowadays
Leray_spectral_sequence
Homotypic spectrum
chromatic spectral sequence is a spectral sequence, introduced by Ravenel (1978), used for calculating the initial term of the Adams spectral sequence for Brown–Peterson
Chromatic_spectral_sequence
Spectral sequence in algebraic topology
the Serre spectral sequence (sometimes Leray–Serre spectral sequence to acknowledge earlier work of Jean Leray in the Leray spectral sequence) is an important
Serre_spectral_sequence
Spectral sequence
algebra, the Grothendieck spectral sequence, introduced by Alexander Grothendieck in his Tôhoku paper, is a spectral sequence that computes the derived
Grothendieck spectral sequence
Grothendieck_spectral_sequence
Stellar classification
main-sequence star (also called a "K-type dwarf" or "orange dwarf") is a main-sequence (core hydrogen-burning) star of spectral type K. The spectral luminosity
K-type_main-sequence_star
Stellar classification
A G-type main-sequence star is a main-sequence star of spectral type G. The spectral luminosity class is V. Such a star has about 0.9 to 1.1 solar masses
G-type_main-sequence_star
In mathematics, Arnold's spectral sequence (also spelled Arnol'd) is a spectral sequence used in singularity theory and normal form theory as an efficient
Arnold's_spectral_sequence
spectral sequence is a spectral sequence, introduced by J. Peter May (1965, 1966). It is used for calculating the initial term of the Adams spectral sequence
May_spectral_sequence
mathematics, the Hodge–de Rham spectral sequence (named in honor of W. V. D. Hodge and Georges de Rham) or Frölicher spectral sequence (named after Alfred Frölicher
Hodge–de Rham spectral sequence
Hodge–de_Rham_spectral_sequence
mathematics known as K-theory, the Quillen spectral sequence, also called the Brown–Gersten–Quillen or BGQ spectral sequence (named after Kenneth Brown, Stephen
Quillen_spectral_sequence
Spectral sequence
In mathematics, the Adams spectral sequence is a spectral sequence introduced by J. Frank Adams (1958) which computes the stable homotopy groups of topological
Adams_spectral_sequence
Topic in mathematics
algebra and number theory, the Lyndon spectral sequence or Hochschild–Serre spectral sequence is a spectral sequence relating the group cohomology of a normal
Lyndon–Hochschild–Serre spectral sequence
Lyndon–Hochschild–Serre_spectral_sequence
Eilenberg–Moore spectral sequence addresses the calculation of the homology groups of a pullback over a fibration. The spectral sequence formulates the
Eilenberg–Moore spectral sequence
Eilenberg–Moore_spectral_sequence
In mathematics, the EHP spectral sequence is a spectral sequence used for inductively calculating the homotopy groups of spheres localized at some prime
EHP_spectral_sequence
Dim, low mass stars on the main sequence
earlier stars. The most recent surveys place the coolest true main-sequence stars into spectral types L2 or L3. At the same time, many objects cooler than about
Red_dwarf
a branch of mathematics, the Čech-to-derived functor spectral sequence is a spectral sequence that relates Čech cohomology of a sheaf and sheaf cohomology
Čech-to-derived functor spectral sequence
Čech-to-derived_functor_spectral_sequence
Generalization of (co)homology using chain complexes
a variety X over a field k, the second spectral sequence from above gives the Hodge–de Rham spectral sequence for algebraic de Rham cohomology: E 1 p
Hyperhomology
In mathematics, the Bockstein spectral sequence is a spectral sequence relating the homology with mod p coefficients and the homology reduced mod p. It
Bockstein_spectral_sequence
Sequence of terms related to the first step of a spectral sequence
five-term exact sequence or exact sequence of low-degree terms is a sequence of terms related to the first step of a spectral sequence. More precisely
Five-term_exact_sequence
Branch of mathematics
topological spaces, and other "tangible" mathematical objects. A spectral sequence is a powerful tool for this. It has played an enormous role in algebraic
Homological_algebra
In mathematics, the Atiyah–Hirzebruch spectral sequence is a spectral sequence for calculating generalized cohomology, introduced by Michael Atiyah and
Atiyah–Hirzebruch spectral sequence
Atiyah–Hirzebruch_spectral_sequence
Main-sequence star of spectral type O
Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main sequence ("dwarfs") Subgiants Giants Red
O-type_main-sequence_star
Relates the homology of two objects to the homology of their product
} In the cases described above, this spectral sequence collapses to give an isomorphism or a short exact sequence. The chain complex of the space X × Y
Künneth_theorem
Concept in algebraic topology
_{i-1}(S^{7}).} Spectral sequences are important tools in algebraic topology for computing (co-)homology groups. The Leray-Serre spectral sequence connects the
Fibration
Finite or infinite ordered list of elements
sequence of vector spaces and linear maps, or of modules and module homomorphisms. In homological algebra and algebraic topology, a spectral sequence
Sequence
Stellar classification distinguished by bright blue luminosity
Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main sequence ("dwarfs") Subgiants Giants Red
B-type_main-sequence_star
Stellar classification
An F-type main-sequence star is a main-sequence, core-hydrogen-fusing star of spectral type F. The spectral luminosity class is V. They have from around
F-type_main-sequence_star
Establish relationships between homology and cohomology theories
\mathbb {Z} /p\mathbb {Z} } , this is a special case of the Bockstein spectral sequence. Let G {\displaystyle G} be a module over a principal ideal domain
Universal_coefficient_theorem
Continuous band of stars that appears on plots of stellar color versus brightness
Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main sequence ("dwarfs") Subgiants Giants Red
Main_sequence
Algebraic topology
is a general source of spectral sequences. It is common especially in algebraic topology; for example, Serre spectral sequence can be constructed by first
Exact_couple
Stellar classification
An A-type main-sequence star is a main-sequence (core hydrogen burning) star of spectral type A. The spectral luminosity class is V. These stars have spectra
A-type_main-sequence_star
sequence is an exact sequence occurring in group cohomology and is a special case of the five-term exact sequence arising from the study of spectral sequences
Inflation-restriction exact sequence
Inflation-restriction_exact_sequence
How spheres of various dimensions can wrap around each other
spectral sequence are themselves quite hard to compute: this is sometimes done using an auxiliary spectral sequence called the May spectral sequence.
Homotopy_groups_of_spheres
nearest stars separated by spectral type. The scope of the list is still restricted to the common main sequence spectral types: M, K, G, F, A, B and
List of nearest stars by spectral type
List_of_nearest_stars_by_spectral_type
Tool in algebraic topology
Grothendieck's 1957 Tôhoku paper. Sheaves, sheaf cohomology, and spectral sequences were introduced by Jean Leray at the prisoner-of-war camp Oflag XVII-A
Sheaf_cohomology
Algebra in algebraic topology
algebras are significant because they can be used to simplify many Adams spectral sequence computations, such as for π ∗ ( k o ) {\displaystyle \pi _{*}(ko)}
Steenrod_algebra
British mathematician (1930–1989)
thesis, written under the direction of Shaun Wylie, was titled On spectral sequences and self-obstruction invariants. He held the Fielden Chair at the
Frank_Adams
Effect in signal processing
discrete sequences, as if a continuous window function has been "sampled". (See an example at Kaiser window.) Window sequences for spectral analysis are
Spectral_leakage
Long exact sequence
It was introduced by Gysin (1942), and is generalized by the Serre spectral sequence. Consider a fiber-oriented sphere bundle with total space E, base
Gysin_homomorphism
Heterogeneous class of stars with unusual spectra
generally lack the O VI lines that are strong in WO spectra. The WN spectral sequence was expanded to include WN2–WN9, and the definitions refined based
Wolf–Rayet_star
relations Serre subcategory Serre functor Serre spectral sequence Lyndon–Hochschild–Serre spectral sequence Serre–Swan theorem Serre–Tate theorem Serre's
List of things named after Jean-Pierre Serre
List_of_things_named_after_Jean-Pierre_Serre
Subject area in mathematics
existence of a spectral sequence like the Atiyah–Hirzebruch spectral sequence in topological K-theory. Quillen's proposed spectral sequence would start from
Algebraic_K-theory
American mathematician
his most famous papers are Periodic phenomena in the Adams–Novikov spectral sequence, which he wrote together with Haynes R. Miller and W. Stephen Wilson
Douglas_Ravenel
Invariant of mathematical knots
a spectral sequence relating Khovanov homology with the knot Floer homology of Peter Ozsváth and Zoltán Szabó (Dowlin 2018). This spectral sequence settled
Khovanov_homology
Soviet and Russian mathematician (1938–2024)
relative isolation. Among other advances he showed how the Adams spectral sequence, a powerful tool for proceeding from homology theory to the calculation
Sergei Novikov (mathematician)
Sergei_Novikov_(mathematician)
Mathematical conjecture
rational homotopy theory, the Halperin conjecture concerns the Serre spectral sequence of certain fibrations. It is named after the Canadian mathematician
Halperin_conjecture
Color evoked by a single wavelength of light in the visible spectrum
A spectral color is a color that is evoked by monochromatic light, i.e. either a spectral line with a single wavelength or frequency of light in the visible
Spectral_color
Differential variety
Vinogradov C {\displaystyle {\mathcal {C}}} -spectral sequence (or, for short, Vinogradov sequence) is a spectral sequence associated to a diffiety, which can
Diffiety
Concept in algebraic topology
exact sequence in group cohomology, and in integration in fibers. It also naturally arises in many spectral sequences; see spectral sequence#Edge maps
Transgression_map
Algebraic tool for computing topological spaces' invariants
Mayer–Vietoris spectral sequence) in the case where the open cover used to compute the Čech cohomology consists of two open sets. This spectral sequence exists
Mayer–Vietoris_sequence
Application of homotopy to algebraic varieties
Eilenberg-Maclane spaces", arXiv:0805.4432 [math.AG] The motivic Adams spectral sequence Motivic chromatic homotopy theory Jardine. (1999) Motivic Symmetric
A¹_homotopy_theory
Invariant of algebraic varieties and of more general schemes
spectral sequence from motivic cohomology to algebraic K-theory for every smooth scheme X over a field, analogous to the Atiyah-Hirzebruch spectral sequence
Motivic_cohomology
Relative importance of certain frequencies in a composite signal
\Delta \tau } The goal of spectral density estimation is to estimate the spectral density of a random signal from a sequence of time samples. Depending
Spectral_density
Polish-American mathematician (1913–1998)
JSTOR 1969365. Eilenberg, Samuel; Moore, John C. (1962), "Limits and spectral sequences", Topology, 1 (1): 1–23, doi:10.1016/0040-9383(62)90093-9, ISSN 0040-9383
Samuel_Eilenberg
Branch of mathematics
Atiyah–Hirzebruch spectral sequence, which makes it very accessible. The only required computations for understanding the spectral sequences are computing
K-theory
Topological invariant in mathematics
covering spaces as special cases, and can be proven by the Serre spectral sequence on homology of a fibration. For fiber bundles, this can also be understood
Euler_characteristic
American mathematician (born 1939)
foundational aspects of spectra. He is known, in particular, for the May spectral sequence and for coining the term operad. May received a Bachelor of Arts degree
J._Peter_May
Largest absolute value of an operator's eigenvalues
mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. More generally, the spectral radius of a bounded
Spectral_radius
On when a morphism of spectral sequences in homological algebra is an isomorphism
introduced by Christopher Zeeman, gives conditions for a morphism of spectral sequences to be an isomorphism. Comparison theorem—Let E p , q r , ′ E p , q
Zeeman's_comparison_theorem
In mathematics, a topological construction
implies that the lower homotopy groups are trivial. Recall there is a spectral sequence for any Serre fibration, such as the fibration K ( π n + 1 ( X )
Postnikov_system
Tools for studying groups based on techniques from algebraic topology
{SL} _{2}(k)} agree for an infinite field k. The Hochschild–Serre spectral sequence relates the cohomology of a normal subgroup N of G and the quotient
Group_cohomology
Concept in mathematics
} of elements in the E r {\displaystyle E_{r}} -page of the Adams spectral sequence contain a permanent cycle, meaning has an associated element in π
Toda_bracket
Algebraic structure
weight n {\displaystyle n} . On the other hand, the Hodge–de Rham spectral sequence supplies H n {\displaystyle H^{n}} with the decreasing filtration
Hodge_structure
Problem in Fourier analysis
The spectral concentration problem in Fourier analysis refers to finding a time sequence of a given length whose discrete Fourier transform is maximally
Spectral concentration problem
Spectral_concentration_problem
Formulation to quantize gauge field theories in physics
D = d + δ. The cohomology groups of (Tot(K), D) are computed using a spectral sequence associated to the double complex ( K ∙ , ∙ , d , δ ) {\displaystyle
BRST_quantization
Branch of mathematics
conjectures Moduli stack of formal group laws Chromatic spectral sequence Adams-Novikov spectral sequence Lurie, J. (2010). "Chromatic Homotopy Theory". 252x
Chromatic_homotopy_theory
Part of a spectrum
Spectral bands are regions of a given spectrum, having a specific range of wavelengths or frequencies. Most often, it refers to electromagnetic bands,
Spectral_band
give examples where the first two terms E1 and E2 of the Frölicher spectral sequence are not isomorphic. As a complex manifold, such an Iwasawa manifold
Iwasawa_manifold
Russian-Italian mathematician (1938–2019)
{\displaystyle {\cal {C}}} -spectral sequence (now known as the Vinogradov spectral sequence). The first term of this spectral sequence gives a unified cohomological
Alexandre Mikhailovich Vinogradov
Alexandre_Mikhailovich_Vinogradov
Mathematics glossary
Abstract homotopy theory Adams 1. John Frank Adams. 2. The Adams spectral sequence. 3. The Adams conjecture. 4. The Adams e-invariant. 5. The Adams
Glossary of algebraic topology
Glossary_of_algebraic_topology
Mathematical conjecture
integers and l is prime, then there is a spectral sequence analogous to the Atiyah–Hirzebruch spectral sequence, starting at E 2 p q = H etale p ( Spec
Quillen–Lichtenbaum conjecture
Quillen–Lichtenbaum_conjecture
Astronomical objects colder than red dwarfs
temperatures that are higher. Old L-subdwarfs with an early L spectral type can be main-sequence stars. The brown dwarf SDSS J0104+1535 (usdL1.5, 0.086 ± 0
L_dwarf
Belgian mathematician
critères de dégénérescence de suites spectrales (Theorem of Lefschetz and criteria of degeneration of spectral sequences). He completed his doctorate at the
Pierre_Deligne
Branch of algebraic topology
X. This holds whenever E is a spin-bundle. The Atiyah-Hirzebruch spectral sequence allows computation of K-groups from ordinary cohomology groups. Topological
Topological_K-theory
Tool to track locally defined data attached to the open sets of a topological space
big theorem in this space is the Hodge decomposition found using a spectral sequence associated to sheaf cohomology groups, proved by Deligne. Essentially
Sheaf_(mathematics)
Signal processing technique
spectral density) of a signal from a sequence of time samples of the signal. Intuitively speaking, the spectral density characterizes the frequency content
Spectral_density_estimation
Structure in algebraic geometry
properties of the Nisnevich topology is the existence of a descent spectral sequence. Let X be a Noetherian scheme of finite Krull dimension, and let Gn(X)
Nisnevich_topology
Concept in differential geometry
P_{E}\to M,} hence the Serre spectral sequence can be applied. From general theory of spectral sequences, there is an exact sequence 0 → E 3 0 , 1 → E 2 0
Spin_structure
Substellar object
Digital Sky Survey (SDSS). This spectral class also contains the coolest main-sequence stars (> 80 MJ), which have spectral classes L2 to L6. As GD 165B
Brown_dwarf
Branch of mathematics
algebra K-theory Lie algebroid Lie groupoid Ramification theory Serre spectral sequence Sheaf Topological quantum field theory Hatcher, Allen. "Algebraic
Algebraic_topology
Constellation in the northern sky
Kaler (28 July 2011). Stars and Their Spectra: An Introduction to the Spectral Sequence. Cambridge University Press. pp. 241–. ISBN 978-0-521-89954-3. Archived
Ursa_Major
British-Lebanese mathematician (1929–2019)
proved analogues of the result at odd primes. The Atiyah–Hirzebruch spectral sequence relates the ordinary cohomology of a space to its generalized cohomology
Michael_Atiyah
Algebraic construct classifying topological spaces
techniques than the definitions might suggest. In particular the Serre spectral sequence was constructed for just this purpose. Certain homotopy groups of
Homotopy_group
French mathematician (1906–1998)
Leray's work of this period proved seminal to the development of spectral sequences and sheaves. These were subsequently developed by many others, each
Jean_Leray
Relates the homology of a fiber bundle with the homologies of its base and fiber
cohomologies of the direct factors. It is a very special case of the Leray spectral sequence. Let π : E ⟶ B {\displaystyle \pi \colon E\longrightarrow B} be a
Leray–Hirsch_theorem
Set of mathematical conjectures proposed by Douglas Ravenel
because of its connection with the convergence of an Adams–Novikov spectral sequence. While opinion has been generally against the truth of the original
Ravenel's_conjectures
American mathematician
American mathematician. The Borel−Moore homology and Eilenberg–Moore spectral sequence are named after him. Moore was born in 1923 in Staten Island, New
John_Coleman_Moore
Mathematical object
Spectral Sequences - Allen Hatcher - contains excellent introduction to spectra and applications for constructing Adams spectral sequence An untitled
Spectrum_(topology)
Type of star that is massive and luminous
Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main sequence ("dwarfs") Subgiants Giants Red
Supergiant
American mathematician (1941–2020)
algebraic topology, he specialised in homotopy theory. The Bousfield-Kan spectral sequence, Bousfield localization of spectra and model categories, and the
Aldridge_Bousfield
American mathematician (1931–2013)
Adams spectral sequence for j ≥ 3 {\displaystyle j\geq 3} . In addition, he made extensive computations of the structure of the Adams spectral sequence and
Mark_Mahowald
Application of K-theory in string theory
quotient by these large gauge transformations. The Atiyah–Hirzebruch spectral sequence constructs twisted K-theory, with a twist given by the NS 3-form field
K-theory_(physics)
Homological construction
formulas otherwise described (not completely faithfully) by complicated spectral sequences. The development of the derived category, by Alexander Grothendieck
Derived_category
Type of star larger than main-sequence but smaller than a giant
Hertzsprung–Russell diagram Spectral type O B A F G K M L T Brown dwarfs White dwarfs Red dwarfs Subdwarfs Main sequence ("dwarfs") Subgiants Giants Red
Subgiant
Operation in algebraic topology
can be used to describe the differentials of the Eilenberg–Moore spectral sequence. The complement of the Borromean rings gives an example where the
Massey_product
resolutions of spectra yielding a tool for constructing the Adams spectral sequence. Essentially, the idea is to take a connective spectrum of finite
Adams_resolution
Modern discipline
secondary calculus are the elements of the first term of the so-called C-spectral sequence, and so on. The simplest diffieties are infinite prolongations of
Secondary calculus and cohomological physics
Secondary_calculus_and_cohomological_physics
British mathematician (1925–2016)
homology and cohomology, introducing what is now known as the Zeeman spectral sequence. This was studied by Clint McCrory in his 1972 Brandeis thesis following
Christopher_Zeeman
SPECTRAL SEQUENCE
SPECTRAL SEQUENCE
Boy/Male
Tamil
Special
Boy/Male
Hindu, Indian
Special
Boy/Male
Indian
Special
Girl/Female
Greek, Indian, Marathi, Turkish
Special
Boy/Male
Hindu, Indian
Special
Girl/Female
Hindu, Indian, Tamil
Special
Boy/Male
Tamil
Saisnigda | ஸாஈஸà¯à®¨à¯€à®•à¯à®¤à®¾
Special
Saisnigda | ஸாஈஸà¯à®¨à¯€à®•à¯à®¤à®¾
Boy/Male
Hindu
Special
Girl/Female
Indian
Special
Boy/Male
Indian, Telugu
Special
Girl/Female
Hindu, Indian, Tamil
Special
Girl/Female
Bengali, Indian, Telugu
Special
Girl/Female
Tamil
Special
Girl/Female
Indian
Special
Girl/Female
Bengali, Indian, Telugu
Special
Girl/Female
Bengali, Indian, Modern
Special
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Muslim, Sindhi, Tamil, Telugu
Special
Girl/Female
Hindu, Indian, Tamil
Special
Boy/Male
Hindu, Indian
Special
Girl/Female
Indian, Telugu
Special
SPECTRAL SEQUENCE
SPECTRAL SEQUENCE
Girl/Female
Tamil
Abhinithi | அபிநீதி
That which is already been performed, Friendship
Female
English
Short form of English Aileen, AILEE means "little Eve."Â
Boy/Male
Arabic
Victory
Boy/Male
Hindu, Indian, Sikh, Sindhi
King's Son; Prince
Girl/Female
Hindu, Indian, Tamil, Telugu
Prayer; Worshipping God
Boy/Male
Tamil
Sayantan | ஸயாஂதநÂ
Brave
Surname or Lastname
English
English : from a late variant of the Norman personal name Baldwin.
Boy/Male
Hindu
Request
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Mythological, Sanskrit, Telugu
One who Brought River Ganga to the Earth; An Ancient King
Boy/Male
Hindu, Indian, Malayalam, Marathi
Protector of Wealth
SPECTRAL SEQUENCE
SPECTRAL SEQUENCE
SPECTRAL SEQUENCE
SPECTRAL SEQUENCE
SPECTRAL SEQUENCE
a.
Having the breast conspicuously colored; as, the pectoral sandpiper.
a.
Of or pertaining to a sector; as, a sectoral circle.
n.
A clasp or a cross worn on the breast.
adv.
In the form or manner of a specter.
a.
Of or pertaining to the breast, or chest; as, the pectoral muscles.
n.
The tarsius, or spectral lemur.
a.
Of or pertaining to the spectrum; made by the spectrum; as, spectral colors; spectral analysis.
n.
A medicine for diseases of the chest organs, especially the lungs.
a.
Limited in range; confined to a definite field of action, investigation, or discussion; as, a special dictionary of commercial terms; a special branch of study.
n.
A covering or protecting for the breast.
a.
Of or pertaining to a specter; ghosty.
n.
One appointed for a special service or occasion.
n.
The several colored and other rays of which light is composed, separated by the refraction of a prism or other means, and observed or studied either as spread out on a screen, by direct vision, by photography, or otherwise. See Illust. of Light, and Spectroscope.
n.
An apparition; a specter.
a.
Relating to, or good for, diseases of the chest or lungs; as, a pectoral remedy.
n.
A luminous appearance, or an image seen after the eye has been exposed to an intense light or a strongly illuminated object. When the object is colored, the image appears of the complementary color, as a green image seen after viewing a red wafer lying on white paper. Called also ocular spectrum.
pl.
of Spectrum
n.
A breastplate, esp. that worn by the Jewish high person.
a.
Of or pertaining to a scepter; like a scepter.
a.
Appropriate; designed for a particular purpose, occasion, or person; as, a special act of Parliament or of Congress; a special sermon.