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the Seifert conjecture states that every nonsingular, continuous vector field on the 3-sphere has a closed orbit. It is named after Herbert Seifert. In
Seifert_conjecture
German mathematician
Horst Schubert. Seifert surface Seifert–van Kampen theorem Seifert conjecture Seifert–Weber space Grattan-Guinness, Ivor (2005-02-11). Landmark Writings
Herbert_Seifert
Polish-American mathematician
1993 work in which she constructed a smooth counterexample to the Seifert conjecture. She has since continued to work in dynamical systems. At Auburn University
Krystyna_Kuperberg
Three dimensional analogue of uniformization conjecture
are Seifert manifolds or atoroidal called the JSJ decomposition, which is not quite the same as the decomposition in the geometrization conjecture, because
Geometrization_conjecture
Topological space
are Seifert fiber spaces, and they account for all compact oriented manifolds in 6 of the 8 Thurston geometries of the geometrization conjecture. A Seifert
Seifert_fiber_space
Russian-American mathematician
for his counterexample (joint with Başak Gürel) to the Hamiltonian Seifert conjecture which constructs a Hamiltonian with an energy level with no periodic
Viktor_Ginzburg
Mathematical space
mathematics, Seifert–Weber space (introduced by Herbert Seifert and Constantin Weber) is a closed hyperbolic 3-manifold. It is also known as Seifert–Weber dodecahedral
3-manifold
the Weinstein conjecture by showing that the embedded contact homology of any contact three-manifold is nontrivial. Seifert conjecture Weinstein, A. (1979)
Weinstein_conjecture
mathematics, Seifert–Weber space (introduced by Herbert Seifert and Constantin Weber) is a closed hyperbolic 3-manifold. It is also known as Seifert–Weber dodecahedral
Seifert–Weber_space
Orientable surface whose boundary is a knot or link
In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is an orientable surface whose boundary is a given knot or link.
Seifert_surface
Conjecture in knot theory relating quantum invariants and hyperbolic geometry
In the branch of mathematics called knot theory, the volume conjecture is an open problem that relates quantum invariants of knots to the hyperbolic geometry
Volume_conjecture
Exception to a proposed general rule
of the Seifert conjecture, the Pólya conjecture, the conjecture of Hilbert's fourteenth problem, Tait's conjecture, and the Ganea conjecture. In 2026
Counterexample
American mathematician
Mathematical Society. Handel, Michael. "One Dimensional Minimal Sets and the Seifert Conjecture ". Annals of Mathematics (2) 111 (1980), number 1, pages 35–66. DOI:10
Michael_Handel
Conjecture pertaining to finite covers of 3-manifold subfields
In the mathematical subfield of 3-manifolds, the virtually fibered conjecture, formulated by American mathematician William Thurston, states that every
Virtually_fibered_conjecture
Alternative mathematical ordering
S2CID 121148668 Bowditch, Brian H. (November 2004), "Planar groups and the Seifert conjecture", Journal für die Reine und Angewandte Mathematik, 2004 (576): 11–62
Cyclic_order
"Contact topology and hydrodynamics. I. Beltrami fields and the Seifert conjecture", Nonlinearity, 13 (2): 441–448, Bibcode:2000Nonli..13..441E, doi:10
Beltrami_vector_field
American mathematician
theory, and 3-manifolds. In 1974, he found a counterexample to the Seifert conjecture that every non-vanishing vector field on the 3-sphere has a closed
Paul_A._Schweitzer
Polish American mathematician
Greg; Kuperberg, Krystyna (1996). "Generalized counterexamples to the Seifert conjecture". Annals of Mathematics. Second Series. 144 (3): 547–576. arXiv:math/9802040
Greg_Kuperberg
American mathematician (1946–2012)
non-Haken non-Seifert-fibered 3-manifolds. These were the first such examples; previously it had been believed that except for certain Seifert fiber spaces
William_Thurston
Kuperberg, mathematician known for creating a counterexample to the Seifert conjecture Nathaniel Thomas Lupton, professor of chemistry William Vann Parker
List of Auburn University people
List_of_Auburn_University_people
Seifert (1907–1969) Mathematician 1935–1975 Eponym of Seifert fiber space, Seifert surface, Seifert-van Kampen theorem, Seifert conjecture, Seifert–Weber
List of Heidelberg University people
List_of_Heidelberg_University_people
Polish-American topologist who found a smooth counterexample to the Seifert conjecture Věra Kůrková (born 1948), Czech expert in neural networks and approximation
List_of_women_in_mathematics
Process in mathematics of decomposing a topological space
either atoroidal or Seifert-fibered. The JSJ decomposition is not quite the same as the decomposition in the geometrization conjecture, because some of the
JSJ_decomposition
along, providing another Seifert surface of reduced complexity. Hence, there are incompressible Seifert surfaces. Every Seifert surface of a link is related
Incompressible_surface
Friedrich Karl Schmidt Herbert Seifert: Seifert fiber space, Seifert surface, Seifert–van Kampen theorem, Seifert conjecture, Seifert–Weber space Paul Stäckel:
Heidelberg University Faculty of Mathematics and Computer Science
Heidelberg_University_Faculty_of_Mathematics_and_Computer_Science
American mathematician topologist
a professor emeritus at Indiana University. In 1982, he posed a conjecture on Seifert surfaces that remained open for 40 years. It was finally solved
Charles Livingston (mathematician)
Charles_Livingston_(mathematician)
Theorem, Flat manifolds, Crystallographic groups Seifert fiber space Heegaard splitting Waldhausen conjecture Compression body Handlebody Incompressible surface
List of geometric topology topics
List_of_geometric_topology_topics
Unique knot with a crossing number of four
ten Dehn surgeries on the figure-eight knot resulted in non-Haken, non-Seifert-fibered irreducible 3-manifolds; these were the first such examples. Many
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Subclass of manifold
closed and have finite fundamental group. William Thurston's elliptization conjecture, proven by Grigori Perelman using Richard Hamilton's Ricci flow, states
Spherical_3-manifold
Dutch mathematician (1903–1996)
three of his students, David van Dantzig (Ph.D. Groningen 1931), Herbert Seifert (Ph.D. Leipzig 1932), and Hans Richter (Ph.D. Leipzig 1936, co-advised
Bartel Leendert van der Waerden
Bartel_Leendert_van_der_Waerden
Milnor conjecture (topology) Milnor map Möbius energy Mutation (knot theory) Physical knot theory Planar algebra Smith conjecture Tait conjectures Temperley–Lieb
List_of_knot_theory_topics
powers conjecture – disproved for exponents 4 and 5 during the 20th century; unsolved for higher exponents Euler's Graeco-Latin square conjecture – proved
List of topics named after Leonhard Euler
List_of_topics_named_after_Leonhard_Euler
Algebraic topology uses abstract algebra to study topological spaces
Homology sphere Homotopy Path (topology) Fundamental group Homotopy group Seifert–van Kampen theorem Pointed space Winding number Simply connected Universal
List of algebraic topology topics
List_of_algebraic_topology_topics
Two interlinked loops with five structural crossings
{\displaystyle {\begin{pmatrix}1&0&0\\-1&1&0\\0&1&-1\end{pmatrix}}} is a possible Seifert matrix, or because of its Conway polynomial, which is ∇ ( z ) = z 3 . {\displaystyle
Whitehead_link
Mathematics concept
Most Seifert fiber spaces have many incompressible tori Manifold decomposition P2-irreducible manifold Agol, Ian (2013). "The virtual Haken conjecture. With
Haken_manifold
Study of systems of inequalitites
semialgebraic mappings. Piecewise polynomial mappings (see the Pierce–Birkhoff conjecture) are also semialgebraic mappings. Computational real algebraic geometry
Real_algebraic_geometry
Finnish mathematician
collective work of about a dozen mathematicians who proved the Seifert fiber space conjecture. In 1992 he was an invited speaker with talk Generalizations
Pekka_Tukia
Mathematical knot
Neuwirth) if there is a 1-parameter family F t {\displaystyle F_{t}} of Seifert surfaces for K {\displaystyle K} , where the parameter t {\displaystyle
Fibered_knot
American mathematician
Differential Geometry 46 (2), pp. 181–235 (1997) "Instanton homology of Seifert fibred homology three spheres", Proceedings of the London Mathematical
Ronald_J._Stern
Canadian-American mathematician (1931–2022)
formula, the Steinhaus–Johnson–Trotter algorithm, and the Lang–Trotter conjecture. He was born in Kingston, Ontario. He died in Princeton, New Jersey on
Hale_Trotter
Algebraic tool for computing topological spaces' invariants
space. In that respect, the Mayer–Vietoris sequence is analogous to the Seifert–van Kampen theorem for the fundamental group, and a precise relation exists
Mayer–Vietoris_sequence
Gives sufficient condition for Dehn filling to result in a negatively curved 3-manifold
atoroidal, non-Seifert-fibered 3-manifold with infinite word hyperbolic fundamental group. Yet again assuming the geometrization conjecture, these manifolds
2π_theorem
Three linked but pairwise separated rings
realize them using circles in three-dimensional space, but it has been conjectured that they may be realized by copies of any non-circular simple closed
Borromean_rings
Mathematical theory of knots
three-dimensional contact manifold ( M 3 , ξ ) {\displaystyle (M^{3},\xi )} and fix a Seifert surface Σ {\displaystyle \Sigma } to K {\displaystyle K} , that is an embedded
Thurston–Bennequin_number
Topological manifold whose homology coincides with that of a sphere
faces together using this identification yields a closed 3-manifold. (See Seifert–Weber space for a similar construction, using more "twist", that results
Homology_sphere
Knot invariant named after Cahit Arf
invariant obtained from a quadratic form associated to a Seifert surface. If F is a Seifert surface of a knot, then the homology group H1(F, Z/2Z) has
Arf_invariant_of_a_knot
Manifold of dimension 3 equipped with a hyperbolic metric
importance in 3-dimensional topology as follows from Thurston's geometrisation conjecture proved by Perelman. The study of Kleinian groups is also an important
Hyperbolic_3-manifold
Simplest non-trivial closed knot with three crossings
The fibre is a once-punctured torus. Since the knot complement is also a Seifert fibred with boundary, it has a horizontal incompressible surface—this is
Trefoil_knot
Invariant of framed knots
pushing points of C along the framing vectors. Given a Seifert surface for a knot, the associated Seifert framing is obtained by taking a tangent vector to
Self-linking_number
Subfield of mathematical topology
algorithm to the 3-sphere recognition algorithm. Determining that the Seifert-Weber 3-manifold contains no incompressible surface has been algorithmically
Computational_topology
1988). "On Heegaard decompositions of torus knot exteriors and related Seifert fibre spaces". Mathematische Annalen. 279 (3): 553–581. doi:10.1007/BF01456287
Tunnel_number
2008 mathematics book
Seifert surfaces, the Poincaré–Hopf theorem, the Brouwer fixed point theorem, Betti numbers, and Grigori Perelman's proof of the Poincaré conjecture.
Euler's_Gem
Mathematical knot with crossing number 5
{\displaystyle {\begin{pmatrix}1&-1\\0&2\end{pmatrix}}} is a possible Seifert matrix, or because of its Conway polynomial, which is ∇ ( z ) = 2 z 2 +
Three-twist_knot
Type of mathematical group
X)-structure on a manifold. Another example is the fundamental group of Seifert manifolds. On the other hand, it is not known whether all fundamental groups
Linear_group
American mathematician
Mathematics, vol. 122, 1985, pp. 335–364 with Stern: Instanton homology of Seifert fibred homology three spheres, Proceedings of the London Mathematical Society
Ronald_Fintushel
include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives and integrals in alternative
List_of_theorems
Branch of mathematics studying (smooth) functions of manifolds
case of dimension 4 is the last open case of the generalized Poincaré conjecture; see Gluck twists. The distinction is because surgery theory works in
Geometric_topology
Discrete group of Möbius transformations
maps. Ahlfors measure conjecture Density theorem for Kleinian groups Ending lamination theorem Tameness theorem (Marden's conjecture) Klein, Felix (1883)
Kleinian_group
Loop seen as a trivial knot
embedded disk, which gives the characterization that only unknots have Seifert genus 0. Similarly, the unknot is the identity element with respect to
Unknot
Class of vitamins
673–685. doi:10.1002/jimd.12009. PMID 30693532. Reinhold A, Westermann M, Seifert J, von Bergen M, Schubert T, Diekert G (November 2012). "Impact of vitamin
Vitamin_B12
classify 3-manifolds and also in proving the higher-dimensional Poincaré conjecture. The table below is a summary of the various manifold-decomposition techniques
Manifold_decomposition
Chemical element with atomic number 31 (Ga)
(3): 548–551. doi:10.1021/ie50519a028. Frenzel, Max; Ketris, Marina P.; Seifert, Thomas; Gutzmer, Jens (March 2016). "On the current and future availability
Gallium
Theory of hyperbolic spacetimes
strengthened from a topological to a smooth context. For this purpose, Seifert’s thesis is cited. However, the proof of this result (published as an article
Geroch's_splitting_theorem
the Seifert–Van Kampen theorem. The main result of the paper on Van Kampen diagrams, now known as the van Kampen lemma can be deduced from the Seifert–Van
Van_Kampen_diagram
Complement of a knot in three-sphere
manifolds. More generally complements of links are Haken manifolds. Knot genus Seifert surface C. Gordon and J. Luecke, "Knots are determined by their Complements"
Knot_complement
Branch of philosophy
(2017). Real Patterns in Biological Explanation. Philosophy of Science. Seifert, V. A. (2022). The Chemical Bond is a Real Pattern. Philosophy of Science
Philosophy_of_science
American mathematician
\mathbb {R} ^{6}} but not in R 5 {\displaystyle \mathbb {R} ^{5}} and Seifert manifolds for fibered knots". Inventiones Mathematicae. 77: 173–184. doi:10
Tim_Cochran
Link formed from a finite number of twisted sections
378–389, doi:10.1007/BFb0099953, MR 0770257 Montesinos, José M. (1973), "Seifert manifolds that are ramified two-sheeted cyclic coverings", Boletín de la
Pretzel_link
Aspect of medical history
Taxonomy. 2006. Retrieved 17 June 2020. Houbraken, J.; Frisvad, J. C.; Seifert, K. A.; Overy, D. P.; Tuthill, D. M.; Valdez, J. G.; Samson, R. A. (December
History_of_penicillin
Unpredictable phenomenon in complex systems
Bibcode:2016npjQM...116024K. doi:10.1038/npjquantmats.2016.24. ISSN 2397-4648. Seifert, Vanessa A. (2022-04-07). "Open questions on emergence in chemistry". Communications
Emergence
Hypothesis that planets with complex life are extremely rare
E.; Smith-Konter, Bridget R.; Burkhard, Liliane; Collins, Geoffrey C.; Seifert, Fiona; Pappalardo, Robert T. (2018). "Morphological mapping of Ganymede:
Rare_Earth_hypothesis
Mathematics textbook
JSJ decomposition of a manifold. This chapter also includes material on Seifert fiber spaces. Chapter four concerns knot theory, knot invariants, thin
Introduction_to_3-Manifolds
reformulations of Cannon's conjecture, (posed by James W. Cannon, although an earlier and more general conjecture, reducing to the Cannon conjecture for compact type
Convergence_group
Mathematical knot with crossing number 5
{\begin{pmatrix}1&-1&0&0\\0&1&-1&0\\0&0&1&-1\\0&0&0&1\end{pmatrix}}} is a possible Seifert matrix, or because of its Conway polynomial, which is ∇ ( z ) = z 4 + 3
Cinquefoil_knot
Knot that bounds an embedded disk in 4-space
are any smoothly slice knots which are not ribbon knots (′Slice-ribbon conjecture′). The conditions locally-flat or smooth are essential in the definition:
Slice_knot
the points 1 and λ on the two sheets of the Riemann surface. From the Seifert–van Kampen theorem, the homology group of the curve is free of rank two
Period_mapping
Study of mathematical knots
knots with up to ten crossings, and what came to be known as the Tait conjectures. This record motivated the early knot theorists, but knot theory eventually
Knot_theory
Knot invariant
This covering can be obtained by cutting the knot complement along a Seifert surface of K and gluing together infinitely many copies of the resulting
Alexander_polynomial
Knot which lies on the surface of a torus in 3-dimensional space
} The complement of a torus knot in the 3-sphere is a Seifert-fibered manifold, fibred over the disc with two singular fibres. Let Y
Torus_knot
Generalized manifold
cusp points. In 3-manifold theory, the theory of Seifert fiber spaces, initiated by Herbert Seifert, can be phrased in terms of 2-dimensional orbifolds
Orbifold
Middle Eastern conflict (2006–2008)
documented case in which a suicide attacker turned out to have been an Iraqi. Seifert, Katherine R.; McCauley, Clark (20 October 2014). "Suicide Bombers in Iraq
Iraqi_civil_war_(2006–2008)
Representation of mathematical space
{\displaystyle \leq 3} . Counterexamples for the triangulation conjecture are counterexamples for the conjecture of the existence of PL-structure of course. Moreover
Triangulation_(topology)
Group whose operation is a composition of braids
topological concepts in the context of quantum physics is in the theory and (conjectured) experimental implementation of the proposed particles anyons. These
Braid_group
How many times curves wind around each other
the integers, corresponding to linking number. This can be seen via the Seifert–Van Kampen theorem (either adding the point at infinity to get a solid
Linking_number
Marine bacteria and marine archaea
07800-11. PMC 3346485. PMID 22344646. Petersen JM, Zielinski FU, Pape T, Seifert R, Moraru C, Amann R, et al. (August 2011). "Hydrogen is an energy source
Marine_prokaryotes
Method of biometric identification
implementation to perform it and so their patent remained conjecture. The roots of this conjecture stretch back even further: in 1892 the Frenchman A. Bertillon
Iris_recognition
Proposed theories of gravity
arXiv:astro-ph/0508048. Bibcode:2005PhRvD..72j1301S. doi:10.1103/PhysRevD.72.101301. Seifert, M. D. (2007). "Stability of spherically symmetric solutions in modified
Alternatives to general relativity
Alternatives_to_general_relativity
Unreproducible object used in digital security
ISBN 978-3-662-48323-7. Helfmeier, Clemens; Nedospasov, Dmitry; Boit, Christian; Seifert, Jean-Pierre (2013). Cloning Physically Unclonable Functions (PDF). IEEE
Physical_unclonable_function
Branch of mathematics
n ) → π n + k S n . {\displaystyle \pi _{k}SO(n)\to \pi _{n+k}S^{n}.} Seifert–van Kampen theorem Homotopy excision theorem Freudenthal suspension theorem
Homotopy_theory
Set with associative invertible operation
is not determined by its lattice of subgroups. See Suzuki 1951. See the Seifert–Van Kampen theorem for an example. An example is group cohomology of a
Group_(mathematics)
Bengali American physicist (born 1931)
Walter Thirring quote: CODENAME GOTT (ISBN 978-3-902406-85-9) published by Seifert Verlag, Vienna, 2011. Mani Bhaumik at Google Scholar Mani L. Bhaumik's
Mani_Lal_Bhaumik
Determining whether a knot is the unknot
classes, which contain the class P. By using normal surfaces to describe the Seifert surfaces of a given knot, Hass, Lagarias & Pippenger (1999) showed that
Unknotting_problem
Analog of the knot group
3 {\displaystyle i,j=1,2,3} and i < j {\displaystyle i<j} . Pick any Seifert surfaces for the respective link components, say, F 1 , F 2 , F 3 {\displaystyle
Link_group
Universe/multiverse, to which authors were major contributors)] and recent conjectures about quantum gravity". 6 April U.S. Space Command, based on information
2022_in_science
American artist (born 1977)
its sociopolitical symbolism. Hi-Fructose Magazine's Daniel 'Attaboy' Seifert says of the "Trash Talking" work, "The message in the art is evident at
Michael_Leavitt_(artist)
the NFL Dick Romney – member of the College Football Hall of Fame George Seifert – former NFL head coach of the San Francisco 49ers and the Carolina Panthers
List of University of Utah people
List_of_University_of_Utah_people
Branch of astronomy using gravitational waves
waves was first suggested by Oliver Heaviside in 1893 and then later conjectured by Henri Poincaré in 1905 as the gravitational equivalent of electromagnetic
Gravitational-wave_astronomy
of the 101st Airborne Division in Kuwait causes the death of CPT Chris Seifert of the Army and Maj Gregory Stone of the Air Force and injuries to 14 others
Timeline of the 2003 invasion of Iraq
Timeline_of_the_2003_invasion_of_Iraq
proved Koebe's conjecture when the number of boundary components is countable; although proved for wide classes of domains, the conjecture remains open
Planar_Riemann_surface
travel, tourism, insurance
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