List questions from differential-topology

Published on 02 Oct 2018 - 12:03

819

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Show that this topology on the sphere is Hausdorff

Published on 25 Mar 2026 - 1:37

132

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Some hypersurface has a positive second fundamental form potentially

Published on 25 Mar 2026 - 3:42

324

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Smooth isotopy preserves orientation

Published on 27 Mar 2026 - 7:24

46

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Decompose a two-manifold into the union of Orientation Reversal Pairs

Published on 03 Oct 2018 - 21:21

783

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A submanifold of a submanifold is a submanifold is the ambient space.

Published on 04 Oct 2018 - 12:22

203

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"winding number" of the map: $M \to S^3$ when $M$ is a non-orientable 3-manifold

Published on 05 Oct 2018 - 2:32

83

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Notation for tensor field contractions

Published on 25 Mar 2026 - 18:59

66

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Why are represenations of differential form unique?

Published on 25 Mar 2026 - 16:01

52

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Why $T_{A}M(n) = M(n)$ and why $T_{f(A)}S(n) = S(n)$ and why $M(n)$ & $S(n)$ are manifolds. (Guillemin & Pollack p.23)

Published on 19 Mar 2026 - 13:05

191

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Unique representation, Bott & Tu, Poincaré's Lemma.

Published on 27 Mar 2026 - 12:03

102

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A difficulty in the proof of partial converse I.(p. 24 in Guillemin & Pollack)

Published on 26 Mar 2026 - 6:30

1.7k

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Prove the quotient map of real projective n space is smooth

Published on 07 Oct 2018 - 1:30

351

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Decomposition of forms in the proof of Poincaré's lemma

Published on 27 Mar 2026 - 12:07

251

Views

k-th exterior power bundle $\Lambda^k(M) = \sqcup_{p\in M}\Lambda^k(\tau(M)_p)$ is a manifold

Published on 25 Mar 2026 - 12:54

List Question

Positive orientation forms is an open set, Orientations of Mantifolds

Show that this topology on the sphere is Hausdorff

Some hypersurface has a positive second fundamental form potentially

Smooth isotopy preserves orientation

Decompose a two-manifold into the union of Orientation Reversal Pairs

A submanifold of a submanifold is a submanifold is the ambient space.

"winding number" of the map: $M \to S^3$ when $M$ is a non-orientable 3-manifold

Notation for tensor field contractions

Why are represenations of differential form unique?

Why $T_{A}M(n) = M(n)$ and why $T_{f(A)}S(n) = S(n)$ and why $M(n)$ & $S(n)$ are manifolds. (Guillemin & Pollack p.23)

Unique representation, Bott & Tu, Poincaré's Lemma.

A difficulty in the proof of partial converse I.(p. 24 in Guillemin & Pollack)

Prove the quotient map of real projective n space is smooth

Decomposition of forms in the proof of Poincaré's lemma

k-th exterior power bundle $\Lambda^k(M) = \sqcup_{p\in M}\Lambda^k(\tau(M)_p)$ is a manifold

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