Question

Topology of the intersection of toric arrangement

score 27 · Answer 1 · 2014-10-16 15:40:43

27

Views

Topology of the intersection of toric arrangement

Published on 16 Oct 2014 - 15:40

score 113 · Answer 2 · 2014-10-16 15:48:45

113

Views

Operations on a smooth vector bundle

Published on 16 Oct 2014 - 15:48

score 266 · Answer 3 · 2014-10-17 00:24:00

266

Views

Tangent bundles of smooth manifolds

Published on 17 Oct 2014 - 0:24

score 124 · Answer 4 · 2014-10-17 01:50:43

124

Views

Submersion preserves openness

Published on 17 Oct 2014 - 1:50

score 431 · Answer 5 · 2014-10-18 09:55:07

431

Views

Pathwise, simple connectedness of real Grassmannian $G(2, 4)$

Published on 18 Oct 2014 - 9:55

score 599 · Answer 6 · 2014-10-18 22:22:08

599

Views

Smoothing Lemma

Published on 18 Oct 2014 - 22:22

score 225 · Answer 7 · 2014-10-19 13:40:46

Prove that there exists a diffeomorphism from an open neighborhood of $Z$ in $N(Z;Y)$ onto an open neighborhood of $Z$ in $Y$.

score 673 · Answer 8 · 2014-10-19 15:46:10

Prove that $N(Z;Y)$ is trivial if and only if there exists a set of $k$ independent functions $g_1,…,g_k$ for $Z$ on some set $U$ in $Y$.

score 891 · Answer 9 · 2014-10-19 18:54:13

Prove that there exists a smooth map $g\colon R\to R$ such that $f(\cos(t),\sin(t))=(\cos(g(t)),\sin(g(t)))$ and satisfying $g(2π)=g(0)+2\pi q$.

score 773 · Answer 10 · 2014-10-19 19:54:01

773

Views

Prove that $\deg_2 (f) \equiv q \mod 2$

Published on 19 Oct 2014 - 19:54

score 118 · Answer 11 · 2014-10-19 19:56:14

118

Views

Problem solving strategies in differential topology

Published on 19 Oct 2014 - 19:56

score 229 · Answer 12 · 2026-03-25 17:42:07

229

Views

A question related to the topology of the level sets of a particular type of smooth functions $f:\mathbb{R}^2\to \mathbb{R}$.

Published on 25 Mar 2026 - 17:42

score 564 · Answer 13 · 2014-10-20 17:44:08

564

Views

Show that if $X$ may be deformed into $Z$ then $X$ and $Z$ are cobordant.

Published on 20 Oct 2014 - 17:44

score 711 · Answer 14 · 2014-10-20 18:10:47

711

Views

Show that the central circle $X$ in the open Mobius band has mod 2 intersection number $I_2(X,X)=1$

Published on 20 Oct 2014 - 18:10

score 2.4k · Answer 15 · 2014-10-22 14:39:05

2.4k

Views

The tangent space of the boundary of a manifold with boundary is a subspace of the tangent space

Published on 22 Oct 2014 - 14:39

List Question

Topology of the intersection of toric arrangement

Operations on a smooth vector bundle

Tangent bundles of smooth manifolds

Submersion preserves openness

Pathwise, simple connectedness of real Grassmannian $G(2, 4)$

Smoothing Lemma

Prove that there exists a diffeomorphism from an open neighborhood of $Z$ in $N(Z;Y)$ onto an open neighborhood of $Z$ in $Y$.

Prove that $N(Z;Y)$ is trivial if and only if there exists a set of $k$ independent functions $g_1,…,g_k$ for $Z$ on some set $U$ in $Y$.

Prove that there exists a smooth map $g\colon R\to R$ such that $f(\cos(t),\sin(t))=(\cos(g(t)),\sin(g(t)))$ and satisfying $g(2π)=g(0)+2\pi q$.

Prove that $\deg_2 (f) \equiv q \mod 2$

Problem solving strategies in differential topology

A question related to the topology of the level sets of a particular type of smooth functions $f:\mathbb{R}^2\to \mathbb{R}$.

Show that if $X$ may be deformed into $Z$ then $X$ and $Z$ are cobordant.

Show that the central circle $X$ in the open Mobius band has mod 2 intersection number $I_2(X,X)=1$

The tangent space of the boundary of a manifold with boundary is a subspace of the tangent space

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