List questions from differential-topology

Published on 11 Apr 2026 - 0:03

71

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A regular surface can't cover any open set of $\mathbb{R}^3$.

Published on 15 Apr 2026 - 3:49

43

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Could I ask where i mistook in using riccati matrix equation?

Published on 12 Apr 2026 - 7:32

51

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If $v(t,x)\in T_x\:\partial M$ for all $(t,x)\in[0,\tau]\times\partial M$, then $f(x)(\text{div}_{\partial M}v_0)(x)+⟨\nabla f(x),v_0(x)⟩=0$

Published on 15 Apr 2026 - 22:01

103

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Trivial tangles and radial Morse functions

Published on 13 Apr 2026 - 5:06

144

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Construct a generic unorientable surfaces of genus $g$

Published on 10 May 2026 - 16:32

475

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Reference Request of Differential Topology

Published on 16 Apr 2026 - 5:56

42

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Does the pushforward $T_a(X)$ of a vector field $X$ on $M$ map to $T_a(X)$ again?

Published on 16 Apr 2026 - 0:06

448

Views

Smooth Jordan-Schönflies Curve Theorem

Published on 17 Apr 2026 - 10:03

83

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How to write the second Stiefel-Whitney class $w_2(TM)$ as an explicit cochain?

Published on 14 Apr 2026 - 16:51

256

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Vector field along immersion - How do you extend, locally, a vector field along an immersion?

Published on 14 Apr 2026 - 8:05

48

Views

Exterior differential equation in 3D

Published on 09 Apr 2026 - 2:14

43

Views

How to visually think about the difference $dw_1 - dw_2$ between two 2-forms?

Published on 16 Apr 2026 - 15:45

68

Views

Partition of Unity involved in proving that $C^{\infty}(U,V)$ is dense in $C_S^r(U,V)$, differential topology

Published on 16 Apr 2026 - 14:14

238

Views

How to prove impossibility of smooth injection from smooth compact $n$-manifold into $\mathbb{R}^n$?

Published on 11 Apr 2026 - 20:01

List Question

A Morse Function with Minimum Number of Critical Points

A regular surface can't cover any open set of $\mathbb{R}^3$.

Could I ask where i mistook in using riccati matrix equation?

If $v(t,x)\in T_x\:\partial M$ for all $(t,x)\in[0,\tau]\times\partial M$, then $f(x)(\text{div}_{\partial M}v_0)(x)+⟨\nabla f(x),v_0(x)⟩=0$

Trivial tangles and radial Morse functions

Construct a generic unorientable surfaces of genus $g$

Reference Request of Differential Topology

Does the pushforward $T_a(X)$ of a vector field $X$ on $M$ map to $T_a(X)$ again?

Smooth Jordan-Schönflies Curve Theorem

How to write the second Stiefel-Whitney class $w_2(TM)$ as an explicit cochain?

Vector field along immersion - How do you extend, locally, a vector field along an immersion?

Exterior differential equation in 3D

How to visually think about the difference $dw_1 - dw_2$ between two 2-forms?

Partition of Unity involved in proving that $C^{\infty}(U,V)$ is dense in $C_S^r(U,V)$, differential topology

How to prove impossibility of smooth injection from smooth compact $n$-manifold into $\mathbb{R}^n$?

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