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Constructing the first Chern class without using the classifying map for line bundles?

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#characteristic-classes
82
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characteristic classes arising from connections are well-defined

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#differential-geometry #vector-bundles #connections #characteristic-classes
212
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A direct proof of the Chern-Weil isomorphism

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#characteristic-classes #classifying-spaces #de-rham-cohomology
440
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Integral class mod 2 reduction, and Stiefel Whitney class

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#algebraic-topology #differential-topology #homology-cohomology #geometric-topology #characteristic-classes
56
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SW class and expression by Whitney fromula

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#differential-geometry #algebraic-topology #differential-topology #characteristic-classes
420
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Stiefel–Whitney class, obstructions and exact sequences

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#algebraic-topology #differential-topology #geometric-topology #fiber-bundles #characteristic-classes
59
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unit element in cohomology and k-theory

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#differential-geometry #algebraic-topology #homology-cohomology #characteristic-classes #topological-k-theory
72
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How to pair the Arf with Stiefel-Whitney class?

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#algebraic-topology #differential-topology #geometric-topology #characteristic-classes #cobordism
128
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Virtual vector bundles, Grothendieck group, and a pair of bundles

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#differential-geometry #algebraic-topology #differential-topology #vector-bundles #characteristic-classes
557
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Why do the first Chern classes of these line bundles span the Dolbeault cohomology group $H^{1,1}(X;\mathbb{R})$?

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#algebraic-geometry #complex-geometry #vector-bundles #characteristic-classes
1.4k
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Chern classes of tangent bundle over the Grassmannian G(2,4)

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#algebraic-geometry #characteristic-classes #intersection-theory #grassmannian
88
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Some questions about the choice of the definition of characteristic classes.

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#differential-geometry #algebraic-geometry #algebraic-topology #characteristic-classes
66
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Submanifold generators that correspond to Stiefel Whitney class of $\mathbb{RP}^n$

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#differential-geometry #algebraic-topology #homology-cohomology #geometric-topology #characteristic-classes
114
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Existence of an element in $K^0$ group, Koszul complexes

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#differential-geometry #algebraic-topology #vector-bundles #characteristic-classes #topological-k-theory
1.1k
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How can it be that the Chern class fully determines a line bundle, but having Chern class zero doesn't imply a line bundle is trivial?

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#algebraic-geometry #complex-geometry #characteristic-classes

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