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Example of a Serre fibration between manifolds which is not a fiber bundle?

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#manifolds #smooth-manifolds #homotopy-theory #fiber-bundles #fibration
67
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Surfaces of revolution as vector bundles

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#smooth-manifolds #fiber-bundles
1.5k
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Prove coordinate-free formula for the exterior derivative using Cartan's magic formula

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#differential-geometry #smooth-manifolds #differential-forms
584
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What does a nonsymmetric connection on $\Bbb R^n$ look like?

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#metric-spaces #differential-topology #riemannian-geometry #smooth-manifolds
63
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Extending local submanifold to global

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#differential-geometry #manifolds #smooth-manifolds
194
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Tangent space of smooth manifold $M=\{(x,x^3,e^{x-1}) : x \in \Bbb{R}\}$ at $(1,1,1)$

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#manifolds #smooth-manifolds #tangent-spaces
2.1k
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What is an Euclidean retraction (Riemannian Optimization)?

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#optimization #manifolds #riemannian-geometry #smooth-manifolds
70
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12.11 Penrose on Differential Forms. $ d(Adx) = dA \wedge dx $

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#manifolds #smooth-manifolds #differential-forms
70
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Criterion for an analytic variety to be a manifold

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#complex-analysis #algebraic-geometry #smooth-manifolds
2.2k
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Give me an example of a topological manifold which is not a smooth manifold.

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#manifolds #smooth-manifolds
101
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Can any form be wedged with another closed form to obtain a non zero top-form?

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#differential-geometry #differential-topology #smooth-manifolds #differential-forms #exterior-algebra
637
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Cobordism and Boundary Theorem (Guillemin-Pollack)

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#manifolds #differential-topology #smooth-manifolds #cobordism
520
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The boundary of an open half-ball is contained in a union of two spheres ? (Lee's smooth manifold))

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#differential-geometry #smooth-manifolds #submanifold
190
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Find the image of a vector field

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#manifolds #differential-topology #smooth-manifolds
164
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Criterion for equivariant maps to be fiber bundles?

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#smooth-manifolds #fiber-bundles #equivariant-maps

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