Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with smooth-manifolds
Search options not deleted
user 144250
Smooth manifolds and smooth functions between them. For manifolds with additional structure, see more specific tags, such as [riemannian-geometry]. For more topological aspects, see [differential-topology].
0
votes
1
answer
121
views
A sufficient condition for a collection of open sets of a manifold to contain all open sets
Question
Let $k\geq 0$ be an integer and let $M$ be a topological $n$-manifold. Let $\mathcal{U}$ be a set of open sets of $M$ which satisfies the following closure properties:
(1). Let $U\subset M$ b …
- 2,292
1
vote
Accepted
A sufficient condition for a collection of open sets of a manifold to contain all open sets
Yes, it is true that $\mathcal{U}$ contains all open sets of $M$. The proof is a minor modification of Weiss's argument, and proceeds in several steps.
Step1
We show that every open set of $M$ homeom …
- 2,292
6
votes
1
answer
280
views
Why does Bott's obstruction theorem imply the vanishing of some cohomology classes of $B\Gam...
Recall that Bott's obstruction for integrability [Bott70] asserts that:
Given a smooth (=$C^\infty$) $m$-manifold $M$ and a completely integrable vector subbundle $E\subset TM$ of rank $m-q$, every p …
- 2,292
6
votes
Accepted
Why does Bott's obstruction theorem imply the vanishing of some cohomology classes of $B\Gam...
This is explained very nicely in [Law77]. Here is a sketch.
We will use the following crucial lemma.
Lemma (Haefliger). Let $M$ be a smooth manifold and let $\mathcal{H}$ be a $\Gamma_q$-structure on …
- 2,292