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Characteristic class

In mathematics, a characteristic class is a way of associating to each principal bundle of a topological space X a cohomology class of X. The cohomology class measures the extent to which the bundle is "twisted" and whether it possesses sections. Characteristic classes are global invariants that measure the deviation of a local product structure from a…

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Overview

Definition

Characteristic numbers

Motivation

Stability

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Characteristic class

Nodes67
Edges66
Triples75
Avg. degree1.97
Density0.029851
Components1

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Characteristic class

Top relations

related to References · 32
Characteristic class → Allen, Annals, Characteristic Classes, Chern, Complex, Dale, Edition, Fibre, Geometry, Hatcher, ISBN, James, John, K-theoryHusemoller, Lock-gray-alt-2, Lock-green, Lock-red-alt-2, Mathematics Studies, McGraw Hill, Milnor
related to Motivation · 15
Characteristic class → Bonnet, Characteristic, Chern, Gauss, Grassmannians, In, Italian, On, Pontryagin, Schubert, Stiefel, The, What, When, Whitney
related to Characteristic numbers · 10
Characteristic class → Characteristic, Chern, Euler, G-bundle, Given, Pontryagin, Some, Stiefel, The, Whitney
related to Stability · 10
Characteristic class → BG, Chern, Concretely, Equivalently, Euler, In, More, Pontryagin, Stiefel, Whitney
related to Definition · 5
Characteristic class → G-bundles, Let, Set, This, Top
is a · 1
Characteristic class → way of associating to each principal bundle of a topological space X a cohomology class of X

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Important terminology

characteristic class classes cohomology displaystyle theory one chern bundle space homotopy manifolds numbers product isbn euler principal work stiefel whitney

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Characteristic classis away of associating to each principal bundle of a topological space X a cohomology class of X0.90text
the orthogonal groupsinstance ofFor the homotopy theory the relevant information is carried by compact subgroups0.80text
unitary groups of Ginstance ofFor the homotopy theory the relevant information is carried by compact subgroups0.80text
Characteristic classrelated to Characteristic numbersCharacteristic0.60section
Characteristic classrelated to Characteristic numbersSome0.60section
Characteristic classrelated to Characteristic numbersStiefel0.60section
Characteristic classrelated to Characteristic numbersWhitney0.60section
Characteristic classrelated to Characteristic numbersChern0.60section
Characteristic classrelated to Characteristic numbersPontryagin0.60section
Characteristic classrelated to Characteristic numbersEuler0.60section
Characteristic classrelated to Characteristic numbersGiven0.60section
Characteristic classrelated to Characteristic numbersG-bundle0.60section

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