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Kirby–Siebenmann class and the 4th Stiefel-Whitney class: $ \operatorname {ks} (M)$ v.s. $w_4(M)$

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#differential-geometry #algebraic-topology #manifolds #geometric-topology #characteristic-classes
64
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Sum formulas for Pontrjagin square and Postnikov square

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#differential-geometry #algebraic-topology #differential-topology #geometric-topology #characteristic-classes
43
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$\Omega_4^{SO}(K(\mathbb{Z}_2,2))$ v.s. $H^4(K(\mathbb{Z}_2,2),U(1))$: Cocycle form

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#algebraic-topology #geometric-topology #group-cohomology #characteristic-classes #cobordism
377
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What is the formula for the Wu class $v_6$ in terms of Stiefel-Whitney classes?

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#algebraic-topology #characteristic-classes
130
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Godbillon-Vey class is independent from the choices involved

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#differential-geometry #vector-bundles #characteristic-classes #foliations
240
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$H^1(M,\mathbb{Z}_2)$: 1st Stiefel Whitney class v.s. fermion eta invariant v.s. spin structure

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#algebraic-topology #differential-topology #characteristic-classes #spin-geometry #cobordism
62
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two versions of the Euler class

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#homology-cohomology #vector-bundles #characteristic-classes #topological-k-theory
92
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Stiefel Whitney classes on the simplex or the simplicial complex

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#algebraic-topology #manifolds #group-cohomology #characteristic-classes
137
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Chern classes of $S^2$

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#differential-geometry #vector-bundles #characteristic-classes
107
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Fiberwise Characteristic Classes

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#reference-request #algebraic-topology #characteristic-classes
187
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Characteristic classes of unit sphere bundle

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#differential-geometry #algebraic-topology #manifolds #smooth-manifolds #characteristic-classes
73
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Extend the fiber of a principal $PSU(n)$-bundle

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#algebraic-topology #characteristic-classes #principal-bundles
443
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Path components of space of almost complex structures

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#differential-geometry #algebraic-topology #differential-topology #symplectic-geometry #characteristic-classes
118
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chern class of bundle in Blochs "Cycles on arithmetic schemes"

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#characteristic-classes #algebraic-vector-bundles
425
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Orientation for a vector bundle

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#algebraic-topology #vector-bundles #characteristic-classes

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