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15
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Direct image of vector bundle under projection map

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#differential-geometry #algebraic-geometry #sheaf-theory #vector-bundles
581
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Hatcher's, tensor product of vector bundles : topology explained

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#general-topology #algebraic-topology #vector-bundles #topological-k-theory
413
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$M$ is orientable iff $\bigwedge^n TM \setminus \{ \text{$0$-section} \}$ has $2$ connected components

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#differential-geometry #differential-topology #smooth-manifolds #vector-bundles
99
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An Orthonormal Frame $(X_i)_i$ which satisfies $\bigtriangledown _{X_i} X_j =0$ at a point

Published on
#riemannian-geometry #vector-bundles #connections #tangent-bundle
47
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notation in vector bundles

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#differential-geometry #notation #vector-bundles
113
Views

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
356
Views

de Rham cohomology of vector bundles: advantages of different definitions of compact vertical cohomology

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#algebraic-topology #differential-topology #homology-cohomology #vector-bundles
55
Views

Degree of curve where matrix of polynomials has rank 1

Published on
#algebraic-geometry #vector-bundles #intersection-theory
51
Views

the form of classes in $K(X)$ [Atiyah]

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#differential-geometry #algebraic-topology #homology-cohomology #vector-bundles #topological-k-theory
835
Views

Clutching function for $S^n$: why a vector bundle?

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#algebraic-topology #vector-bundles #topological-k-theory
114
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Grassmannian manifold and corresponding vector field

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#vector-bundles #grassmannian
88
Views

Question on Kahler geometry: Kahler form and $\mathcal{O}_X(1)$

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#algebraic-geometry #complex-geometry #vector-bundles
123
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Equivalence of definitions of a vector bundle

Published on
#differential-topology #vector-bundles #fiber-bundles
35
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inverses in the definition of vector bundle from principal bundle

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#differential-geometry #vector-bundles
394
Views

How to show that vector field is continuous?

Published on
#differential-geometry #manifolds #differential-topology #vector-bundles #tangent-bundle

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