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15
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Extending a monomorphism of bundles, Lemma 7.3, Atiyah, Shapiro

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#algebraic-topology #differential-topology #vector-bundles #fiber-bundles
39
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An isomorphism of vector bundles over a manifold, $K(X)$,

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#reference-request #algebraic-topology #differential-topology #vector-bundles #k-theory
78
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A Topological Invariant for $\pi_3(U(n))$

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#multivariable-calculus #algebraic-topology #differential-topology #lie-groups #vector-bundles
113
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Does $\nabla g=\omega(\cdot) g$ imply $\nabla$ is metric w.r.t a conformal rescaling of $g$?

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#riemannian-geometry #examples-counterexamples #vector-bundles #conformal-geometry #connections
71
Views

General tips for showing that subspaces "vary continuously"

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#differential-geometry #differential-topology #vector-bundles
173
Views

1-form sufficiently $C^1$-close to the zero section

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#differential-geometry #vector-bundles #symplectic-geometry
125
Views

Vector bundle over linear maps with fixed rank

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#algebraic-geometry #vector-bundles
222
Views

Does existence of a parallel section on $E$ imply local existence of a parallel section on $\bigwedge^k E$?

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#differential-geometry #vector-bundles #curvature #exterior-algebra #connections
60
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Let $B$ be a vector bundle over a compact metric space $X$. Is there always a linear bundle automorphism that covers $f \in \mbox{Homeo}(X)$?

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#real-analysis #general-topology #vector-bundles
427
Views

Two definitions of a connection

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#differential-geometry #riemannian-geometry #vector-bundles
964
Views

How i x j= k (vector) BUT ixj = (i)(j) (sin90) = (1)(1)(1) = 1 (Scalar)

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#vector-spaces #vector-analysis #vector-bundles #vector-fields
898
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Constructing the flat vector bundle associated to a given linear representation of the fundamental group

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#differential-geometry #vector-bundles #fundamental-groups #connections
628
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Every line bundle on a complex algebraic curve has a meromorphic section

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#algebraic-geometry #complex-geometry #vector-bundles #riemann-surfaces
196
Views

Complex structures on $TM$ and $T^*M$

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#differential-geometry #complex-geometry #vector-bundles
62
Views

Can vector bundle be thought of as below?

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#differential-geometry #smooth-manifolds #vector-bundles

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