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gptkbp:instanceOf
|
gptkb:mathematical_concept
|
|
gptkbp:appliesTo
|
real vector bundles
|
|
gptkbp:category
|
gptkb:mathematics
gptkb:topology
|
|
gptkbp:coefficientRing
|
gptkb:Z/2Z
|
|
gptkbp:cohomologyDegree
|
i (for w_i)
|
|
gptkbp:cohomologyGroup
|
H^i(X; Z/2Z)
|
|
gptkbp:detects
|
orientability
spin structures
vector bundle triviality
|
|
gptkbp:field
|
gptkb:topology
|
|
gptkbp:firstClassDetects
|
orientability
|
|
gptkbp:hasFirstClassLounge
|
w_1
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Stiefel–Whitney classes
|
|
gptkbp:introducedIn
|
1930s
|
|
gptkbp:namedAfter
|
gptkb:Hassler_Whitney
gptkb:Eduard_Stiefel
|
|
gptkbp:relatedTo
|
gptkb:Pontryagin_classes
gptkb:Chern_classes
Euler class
|
|
gptkbp:satisfies
|
gptkb:Whitney_sum_formula
naturality
w_0 = 1
w_i = 0 for i > n (n = rank of bundle)
|
|
gptkbp:secondClass
|
w_2
|
|
gptkbp:secondClassDetects
|
spin structure
|
|
gptkbp:totalClass
|
w
|
|
gptkbp:type
|
characteristic class
|
|
gptkbp:usedIn
|
differential topology
cobordism theory
obstruction theory
|
|
gptkbp:bfsParent
|
gptkb:Pontryagin_classes
gptkb:Chern–Weil_theory
gptkb:characteristic_classes
|
|
gptkbp:bfsLayer
|
6
|