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Classifying space

In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e., a topological space all of whose homotopy groups are trivial) by a proper free action of G. It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the…

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Classifying space

Nodes85
Edges84
Triples64
Avg. degree1.98
Density0.023529
Components1

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Classifying space

Top relations

related to Examples · 16
Classifying space → Alternatively, Artin, BS1, CAT, Conf, CP, EO, Gr, Here, Hilbert, RP, S1, Stiefel, The, The Grassmannian, UConf
related to Formalism · 12
Classifying space → Assume, BG, CW, EG, Eilenberg, G-bundle, G-bundles, In, MacLane, That, The, We
related to Motivation · 10
Classifying space → An, C-bundle, C-bundles, G-bundles, In, Taking, The, This, What, When
related to References · 10
Classifying space → Algebraic Topology, Chicago Press, Classifying, Concise Course, EMS Press, Encyclopedia, ISBN, Mathematics, May, University
has application · 9
Classifying space → An, As, BG, Bott, Cartan's, EG, Hilbert, Lie, This
see also · 5
Classifying space → BO, BU, Classifying, SO, SU

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Important terminology

space classifying group displaystyle homotopy bg mathbb topological contractible eg spaces infty groups cyclic theory principal fundamental category also circle

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Lie groupsinstance offor interesting groups G0.80text
the unitary groups that are of greatest interestinstance ofa much more hands-on approach to the theory is possible for cases0.80text
Classifying spacehas applicationThis0.60section
Classifying spacehas applicationBG0.60section
Classifying spacehas applicationLie0.60section
Classifying spacehas applicationCartan's0.60section
Classifying spacehas applicationAs0.60section
Classifying spacehas applicationBott0.60section
Classifying spacehas applicationAn0.60section
Classifying spacehas applicationEG0.60section
Classifying spacehas applicationHilbert0.60section
Classifying spacerelated to ExamplesThe0.60section

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