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15
211
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Induced Connection on Vector Bundle from Principal Bundle

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#vector-bundles #connections #principal-bundles
307
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A criterion for non-orientability of a 3-manifold

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#manifolds #differential-topology #vector-bundles
87
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Show that $\mathbb{CP}^{2n}$ is not the boundary of a $4n+1$ dimensional Manifold using Chern classes

Published on
#homology-cohomology #complex-geometry #vector-bundles #characteristic-classes
114
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Gauss-Bonnet theorem for vector bundles on manifolds with boundary

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#vector-bundles #curvature #characteristic-classes #manifolds-with-boundary
845
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The idea of a bundle chart and bundle atlas.

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#differential-geometry #riemannian-geometry #intuition #vector-bundles #motivation
19
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Why is $c((n+1)H_n^\ast) = c(H_n^\ast)^{n+1}$ for the total Chern class c.

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#complex-geometry #vector-bundles #projective-space #characteristic-classes
228
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Proving both definitions of vertical bundle are the same

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#differential-geometry #vector-bundles
240
Views

Integrable subbundle

Published on
#smooth-manifolds #closed-form #vector-bundles
99
Views

Cupping with a zero class can give a non-trivial class in cohomology with local coefficients?

Published on
#differential-geometry #algebraic-topology #differential-topology #vector-bundles #geometric-topology
346
Views

Why does the dual of a vector bundle use the inverse transpose?

Published on
#vector-bundles #complex-manifolds
50
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Clarification of statement

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#algebraic-topology #vector-bundles #k-theory #topological-k-theory #pullback
65
Views

Tangent bundle of a fiber bundle

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#differential-geometry #vector-bundles #fiber-bundles #tangent-bundle
844
Views

Why does a vector bundle have the same first Chern class as its determinant bundle?

Published on
#vector-bundles #characteristic-classes
470
Views

Are vector bundles with isomorphic determinant bundles isomorphic?

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#vector-bundles #exterior-algebra
98
Views

about the subbundle in complex geometry by daniel huybrechts

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#complex-geometry #vector-bundles

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