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Euler class as obstruction to have a never vanishing cross section

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#algebraic-topology #differential-topology #characteristic-classes #obstruction-theory
195
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$W$ spin implies $\partial W$ spin

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#algebraic-topology #vector-bundles #characteristic-classes #manifolds-with-boundary #spin-geometry
437
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Examples of 4-manifolds with nontrivial third Stiefel-Whitney class $w_3$.

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#algebraic-topology #characteristic-classes #4-manifolds
42
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Inverse problem : Finding a vector bundle (resp. with connection), given its characteristic class (resp. differential character)

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#differential-geometry #reference-request #algebraic-topology #vector-bundles #characteristic-classes
300
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Todd class of a two-dimensional bundle

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#differential-geometry #algebraic-topology #complex-geometry #characteristic-classes
564
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Chern class cohomology coefficients complex/real/integral?

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#differential-geometry #characteristic-classes #de-rham-cohomology
185
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Chern class of a principal $G$ bundle for a compact Lie group $G$

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#differential-geometry #characteristic-classes #de-rham-cohomology
36
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Ring isomorphism between $H^*(G_n(\Bbb F^\infty); R)$ and Ring of characteristic classes

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#algebraic-topology #differential-topology #homology-cohomology #characteristic-classes
61
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A "natural homomorphism" $H^n(B; \Bbb Z) \rightarrow H^n(B; \Bbb Z_2)$.

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#algebraic-topology #definition #differential-topology #vector-bundles #characteristic-classes
104
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Isomorphism of bundles , Madsen's Calculus to Cohomology

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#algebraic-topology #definition #differential-topology #vector-bundles #characteristic-classes
301
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Chern class of holomorphic symplectic manifold

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#differential-geometry #complex-geometry #symplectic-geometry #characteristic-classes
53
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Characteristic classes for $P \rightarrow G \rightarrow G/P$

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#lie-groups #homology-cohomology #characteristic-classes #principal-bundles
123
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Can we detect non-trivial bundles using characteristic classes for a custom structure group?

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#algebraic-topology #fiber-bundles #characteristic-classes
370
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Criteria of a real vector bundle to be Stably trivial

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#general-topology #algebraic-topology #differential-topology #vector-bundles #characteristic-classes
188
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Dual Stiefel-Whitney class $\overline{w}_{n-1}$ vanishes if $n$ is not a power of 2

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#algebraic-topology #characteristic-classes

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