List questions from differential-topology

Published on 11 Apr 2026 - 19:17

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Poincaré-Hopf Theorem for manifolds with boundary in Milnor's book

Published on 26 Mar 2026 - 6:08

832

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Euler Characteristic of fiber bundle using Differential Geometry

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1.6k

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What is the gentlest notes/book of intro differential topology?

Published on 15 Apr 2026 - 2:02

386

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Prove every compact $1$-manifold with boundary always has an even number of boundary points.

Published on 27 Mar 2026 - 13:03

218

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Understanding manifold

Published on 09 Apr 2026 - 9:35

367

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Does the smooth homotopy between diffeomorphisms have to be through diffeomorphisms in order to induce the same equivalence class of cobordisms?

Published on 25 Mar 2026 - 22:06

440

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Can every linear map between tangent spaces be realized as a differential of a map?

Published on 11 Apr 2026 - 19:31

334

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Fundamental Theorem of Calculus for Differential Forms. Conditions?

Published on 11 Apr 2026 - 20:45

1.3k

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Tangent Space of matrices with same rank

Published on 15 Apr 2026 - 15:08

491

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To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$

Published on 17 Apr 2026 - 6:37

436

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Coordinates/charts for the space of k-tuples of orthonormal vectors (a.k.a. Stiefel manifold)

Published on 15 Apr 2026 - 14:11

74

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When does a frame on $\mathbb{R}^n$ arise from a coordinate system?

Published on 10 Apr 2026 - 23:54

328

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3d analog to the Klein bottle

Published on 13 Apr 2026 - 5:47

67

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$G$ is a Lie group and $M$ a manifold. What does it mean that $G$ acts as a group of automorphism on $H^p (M, \mathbb{R} )$?

Published on 25 Mar 2026 - 13:13

List Question

An immersion has constant rank in some neighborhood

Poincaré-Hopf Theorem for manifolds with boundary in Milnor's book

Euler Characteristic of fiber bundle using Differential Geometry

What is the gentlest notes/book of intro differential topology?

Prove every compact $1$-manifold with boundary always has an even number of boundary points.

Understanding manifold

Does the smooth homotopy between diffeomorphisms have to be through diffeomorphisms in order to induce the same equivalence class of cobordisms?

Can every linear map between tangent spaces be realized as a differential of a map?

Fundamental Theorem of Calculus for Differential Forms. Conditions?

Tangent Space of matrices with same rank

To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$

Coordinates/charts for the space of k-tuples of orthonormal vectors (a.k.a. Stiefel manifold)

When does a frame on $\mathbb{R}^n$ arise from a coordinate system?

3d analog to the Klein bottle

$G$ is a Lie group and $M$ a manifold. What does it mean that $G$ acts as a group of automorphism on $H^p (M, \mathbb{R} )$?

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