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topology, a Postnikov square is a certain cohomology operation from a first cohomology group H1 to a third cohomology group H3, introduced by Postnikov (1949)
Postnikov_square
Soviet mathematician (1927–2004)
1985; 374 pp. Postnikov system Postnikov square Sacksteder, Richard (1970). "Review of The variational theory of geodesics by M. M. Postnikov". Bulletin
Mikhail_Postnikov
Surname list
Mikhail Postnikov (1927–2004), Russian mathematician Postnikov square Postnikov system Pyotr Postnikov (1666–1703), Russian diplomat Stanislav Postnikov (1928–2012)
Postnikov
Shape with four equal sides and angles
Proposition 14. Online English version by David E. Joyce. Postnikov, M. M. (2000). "The problem of squarable lunes". The American Mathematical Monthly. 107 (7):
Square
work of Pontryagin, Postnikov, and Norman Steenrod, who first defined the Pontryagin square, Postnikov square, and Steenrod square operations for singular
Cohomology_operation
Geometric construction
particular, there are no other constructible squarable lunes. Postnikov, M. M. (2000), "The problem of squarable lunes", American Mathematical Monthly, 107
Lune_of_Hippocrates
Area interpreted positively or negatively
giving a negative hyperbolic angle as a negative sector area. Mikhail Postnikov's 1979 textbook Lectures in Geometry appeals to certain geometric transformations
Signed_area
Relation between Lie algebras depicted as a square
Freudenthal's Magic Square". Journal of Algebra. 239 (2): 477–512. arXiv:math.AG/9908039. doi:10.1006/jabr.2000.8697. S2CID 16320642. Postnikov, M. (1986), Lie
Freudenthal_magic_square
Algebra in algebraic topology
Malygin, S.N.; Postnikov, M.M. (2001) [1994], "Steenrod reduced power", Encyclopedia of Mathematics, EMS Press Malygin, S.N.; Postnikov, M.M. (2001) [1994]
Steenrod_algebra
Topological space with only one nontrivial homotopy group
be regarded as a building block for CW-complexes via fibrations in a Postnikov system. These spaces are important in many contexts in algebraic topology
Eilenberg–MacLane_space
1093/qmath/13.1.55, ISSN 0033-5606, MR 0140103 Malygin, S.N.; Postnikov, M.M. (2001) [1994], "Pontryagin square", Encyclopedia of Mathematics, EMS Press Pontryagin
Pontryagin cohomology operation
Pontryagin_cohomology_operation
Geometric structure used in certain particle interactions
Nima; Bourjaily, Jacob L.; Cachazo, Freddy; Goncharov, Alexander B.; Postnikov, Alexander; Trnka, Jaroslav (2012). "Scattering Amplitudes and the Positive
Amplituhedron
Soviet mathematician (1908–1988)
Vladimir Boltyansky, Revaz Gamkrelidze, Yevgeny Mishchenko, Mikhail Postnikov, Vladimir Rokhlin, and Mikhail Zelikin. Pontryagin participated in a few
Lev_Pontryagin
Soviet mathematician (1894–1947)
Archived from the original (PDF) on 2006-02-09. Postnikov, M. M. (2000), "The problem of squarable lunes", American Mathematical Monthly, 107 (7): 645–651
Nikolai_Chebotaryov
Mathematical connection between field theory and group theory
Number Theory. Berlin, New York: Springer-Verlag. ISBN 978-0-387-94225-4. Postnikov, M. M. (2004). Foundations of Galois Theory. Dover Publications. ISBN 0-486-43518-0
Galois_theory
U.S. state
Русское поселение на Аляске в XVII в.? "Природа". М., 1992. No. 4. С.67–69. Postnikov, Alexey V. (2000). "Outline of the History of Russian Cartography". Regions:
Alaska
data used to classify the structure of the category, it is given by the Postnikov invariant. For an Abelian 2-group A {\displaystyle \mathbb {A} } and a
Abelian_2-group
Non-associative algebras with positive-definite quadratic form
11 Herstein 1968, pp. 141–144 See: Faraut & Koranyi 1994, pp. 88–91 Postnikov 1986 Albert, A. A. (1934), "On a certain algebra of quantum mechanics"
Hurwitz's theorem (composition algebras)
Hurwitz's_theorem_(composition_algebras)
Algebraic field extension
Springer-Verlag. doi:10.1007/978-1-4612-0853-2. ISBN 978-0-387-94225-4. MR 1282723. Postnikov, Mikhail Mikhaĭlovich (2004). Foundations of Galois Theory. With a foreword
Galois_extension
Russian cosmonaut and politician (born 1937)
the USSR and Russia. Novopromyshna Square in Tver was renamed Tereshkova Square in 1963. In 1967, Gregory Postnikov [ru] created a sculpture of Tereshkova
Valentina_Tereshkova
Infinite-dimensional group in topology
string group is an entry in the Whitehead tower (dual to the notion of Postnikov tower) for the orthogonal group: ⋯ → Fivebrane ( n ) → String ( n
String_group
Mathematical concept
the Serre spectral sequence, Freudenthal suspension theorem, and the Postnikov tower). The map comes from the fiber bundle S 1 ↪ S 2 n − 1 ↠ C P n −
Complex_projective_space
Particular kind of exponential sum
and the exponent α increases to infinity (this case was studied by A.G. Postnikov by means of the method of Ivan Matveyevich Vinogradov). In the 1990s Anatolii
Kloosterman_sum
Danish mathematician and astronomer (1801–1885)
1832-01-01. doi:10.1515/crll.1832.8.298. ISSN 0075-4102. Postnikov, M. M. (2000), "The problem of squarable lunes", American Mathematical Monthly, 107 (7): 645–651
Thomas Clausen (mathematician)
Thomas_Clausen_(mathematician)
Polytope whose vertices represent permutations
totaux", Mathématiques, Informatique et Sciences Humaines, 112: 49–53. Postnikov, Alexander (2009), "Permutohedra, associahedra, and beyond", International
Permutohedron
member of the adjudication committee Alexander Kotov; leader of the group Postnikov; a private doctor from Moscow; and Botvinnik's wife and young daughter
World_Chess_Championship_1948
Russian journalist (born 1984)
demonstrations against election fraud. His coverage of the 2010 Manezhnaya Square riots and the 2011-2013 protests became widely cited. He was among the first
Ilya_Varlamov
Russian general (born 1964)
of the Main Directorate Semyonov Bukreyev Kormiltsev Maslov Boldyrev Postnikov Chirkin Istrakov Salyukov Mordvichev Chiefs of the Main Staff and First
Aleksandr_Lapin_(general)
Bronze statue in Germany
was presumably created in the atelier of the Soviet sculptor Grigory Postnikov (Григорий Николаевич Постников, 1914–1978). Other sources name Nikolai
Statue of Joseph Stalin, Berlin
Statue_of_Joseph_Stalin,_Berlin
Orthodox cathedral in Samara, Russia
for both the dome and bell tower were manufactured in Moscow by A.M. Postnikov's firm. The main dome's cross, costing 2,920 rubles, measured 9 arshins
Cathedral of Christ the Saviour (Samara)
Cathedral_of_Christ_the_Saviour_(Samara)
Alexander Ivanov (1806–1858) neoclassical painter (portrait by Sergey Postnikov [ru]) Sergei Ivanov (1864–1910) history painter, realist, graphic artist
List_of_Russian_artists
Encyclopedia of Life Support Systems. Vol. 4. Bogdanova; Bibikova; De Waele; Postnikov (2007). "Volgo-Uralia: a large piece of the global Archaean framework"
Geology_of_Russia
Study of geometry using a coordinate system
(2nd Ed.), Reading: Addison Wesley Longman, ISBN 0-321-01618-1 Mikhail Postnikov (1982) Lectures in Geometry Semester I Analytic Geometry via Internet
Analytic_geometry
Architecture school in Tomsk, Russia
(1952—1953), Zhestkov S.V. (1953—1955), Damanskii L.M. (1955—1958), Postnikov M.V. (1958—1968), Rogov G.M. (1968—2005 гг.), Slobodskoi M.I. (2005—2012)
Tomsk State University of Architecture and Construction
Tomsk_State_University_of_Architecture_and_Construction
Russian literary figure of 19th century
with barely controlled sobs. Alexei Stepanovich told Archbishop Gregory (Postnikov) of Kazan: "The other day, by God's will, in the sixteenth year of our
Ekaterina_Khomyakova
2009–2017 armed conflict in Russia
Valery Gerasimov Nikolai Makarov Oleg Salyukov Vladimir Chirkin Aleksandr Postnikov Vladimir Boldyrev Ramzan Kadyrov Vladimir Vasilyev Ramazan Abdulatipov
Insurgency in the North Caucasus
Insurgency_in_the_North_Caucasus
Russian mathematician (1937–2008)
{\displaystyle \alpha } increases to infinity (this case was studied by A. G. Postnikov by means of the method of Vinogradov). Karatsuba's method makes it possible
Anatoly_Karatsuba
Russian general (born 1955)
Staff Nikolai Makarov. He commanded the annual Victory Day Parade on Red Square four times from 2009 to 2012. On 28 April 2012, Gerasimov was appointed
Valery_Gerasimov
Organisation that produces maps and geographic information of a country
Archived from the original (PDF) on 7 August 2011. Retrieved 6 June 2011. Postnikov, Alexey (2002). "Maps for Ordinary Consumers versus Maps for the Military:
National_mapping_agency
Russian retired army general (born 1955)
President Vladimir Putin. Salukov has also overseen military parades on Red Square in Moscow on Victory Day from 2014 to 2025. Salyukov was honored with the
Oleg_Salyukov
Demonstrations in Russia
17,710 (2010 census); An unsanctioned rally occurred in Salavat Yulayev Square in the Bashkir capital of Ufa on 19 January 2024. The National Guard and
2024_Bashkortostan_protests
This gives an associated homotopy type X with π1(X)=ℤ2 and π2(X)=ℤ4 Its postnikov invariant can be determined by the class of Q8→ℤ4 in the group cohomology
Double_groupoid
Harry Potter parodies A Boy Named Harry and his Dog Potter, by Valentin Postnikov. Harry Cover (pronounced like haricots verts, French for green beans)
Parodies_of_Harry_Potter
Ethnic minority group in Kazakhstan
(footballer) Stas Pokatilov Aleksei Popov (footballer, born 1978) Yevgeny Postnikov Aleksey Rodionov Denis Rodionov Mikhail Rozhkov Maksim Samorodov Grigory
Russians_in_Kazakhstan
City in Donetsk Oblast of Ukraine
and stands 1.5 metres tall on a 4.5 metre pedestal designed by Hryhorii Postnikov and Yuriy Lapin. There are also multiple war memorials located within
Yenakiieve
Russian general (born 1973)
of the Main Directorate Semyonov Bukreyev Kormiltsev Maslov Boldyrev Postnikov Chirkin Istrakov Salyukov Mordvichev Chiefs of the Main Staff and First
Rustam_Muradov
Land forces of the Russian Armed Forces
(2001–2004) Aleksei Maslov (2004–2008) Vladimir Boldyrev (2008–2010) Aleksandr Postnikov-Streltsov (2010–2012) Vladimir Chirkin (2012–2013) Sergei Istrakov (2013–2014
Russian_Ground_Forces
Russian politician and lieutenant general
non-residential building - 95 square meters. Matovnikov's wife owns two apartments with an area of 38.1 and 104.7 square meters. List of Heroes of the
Aleksandr_Matovnikov
= 0 {\displaystyle h(X)=0} , then h {\displaystyle h} vanishes on any Postnikov section of X {\displaystyle X} . This follows from a theorem that states
Nilpotent_space
Branch of mathematics
coefficient theorem Dold–Thom theorem See also: Characteristic class, Postnikov tower, Whitehead torsion There are several specific theories simple homotopy
Homotopy_theory
Bosnian film and theatre director (born 1969)
Rappaport Villqist's Helver's Night Loher's Adam Geist Nick Wood's Warrior's Square Głowacki's The Fourth Sister Martin McDonagh's Cripple Billy "Dino Mustafić
Dino_Mustafić
Open convex self-dual cones
Theorem 12 Faraut & Koranyi 1994, pp. 42, 153–154 See: Freudenthal 1985 Postnikov 1986 Faraut & Koranyi 1994 Springer & Veldkamp 2000 See: Freudenthal 1985
Symmetric_cone
Former Russian Empire fortress
gradually demolished as Yekaterinburg expanded into the 19th century. Postnikov, S., and E. Vityuk. "Creation Yekaterinburg as an ideal City-fortress
Yekaterinburg_fortress
Mathematics glossary
5. Poincaré homology sphere. Pontrjagin–Thom construction Postnikov system A Postnikov system is a sequence of fibrations, such that all preceding manifolds
Glossary of algebraic topology
Glossary_of_algebraic_topology
Serbian playwright and university professor (born 1970)
Olja Bećković's Utisak nedelje talk programme on Studio B, Srbljanović squared off against her former Pogledi editor-in-chief Miloslav Samardžić over
Biljana_Srbljanović
Special tangential structure
projective space H P ∞ {\displaystyle \mathbb {H} P^{\infty }} and through its Postnikov tower projects onto the Eilenberg–MacLane space K ( Z , 4 ) {\displaystyle
Spinh_structure
Chemical compound
1038/s41467-019-12831-0. ISSN 2041-1723. PMC 6820771. PMID 31664018. Fraser, James P.; Postnikov, Pavel; Miliutina, Elena; Kolska, Zdenka; Valiev, Rashid; Švorčík, Vaclav;
Molybdenum_ditelluride
Military unit
the 81st Guards Rifle Division in the area of Blizhniaia Igumenka and Postnikov and by day's end had taken Dalniaia Igumenka and Shishino. 2. I order:
375th_Rifle_Division
District in Vologda Oblast, Russia
with Verkhovazhsky District in the west. The area of the district is 5,200 square kilometers (2,000 sq mi). Its administrative center is the rural locality
Tarnogsky_District
travel, tourism, insurance
POSTNIKOV SQUARE
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