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 differential-topology
Search options answers only
not deleted
user 6646
The study of differentiable manifolds and differentiable maps. One fundamental problem is that of classifying manifolds up to diffeomorphism. Differential topology is what Poincaré understood as topology or “analysis situs”.
2
votes
Accepted
Relative de rham cohomology with compact support
Not necessarily. For simplicity, let's assume a closed manifold $M$ and a closed submanifold $P$. Then all forms automatically have closed support and the de Rham cohomology is isomorphic to singular …
- 5,544
4
votes
Accepted
Whitney stratifications of hypersurfaces
In order for transversality to make sense, I assume that X is contained in an ambient manifold? Assuming so, the following statement is on page 37 of Goresky and MacPherson's Stratified Morse Theory:
…
- 5,544
6
votes
Accepted
references / general idea of kervaire invariant problem
Here's a recent survey article by Victor Snaith:
http://chucha.math.cinvestav.mx/morfismos/v13n2/arfsurveyMFMS.pdf
(I think there's also a copy on the arxiv)
- 5,544
5
votes
Books in advanced differential topology
Avoiding suggestions already made:
Guillemin and Pollack, Differential Topology, is a classic.
You can also find pieces of a lot of these things in books that are a bit broader, for example:
Topology …
- 5,544
2
votes
Accepted
Relation between cohomological dimensions of manifolds
By Bredon's Sheaf Theory, Proposition II.16.15, if $X$ is locally paracompact then $\dim_L X\leq \dim_{\mathbb Z}X$ for any ring $L$ with unit. So that should answer the question about the relation be …
- 5,544
10
votes
Exotic smooth structures on Lie groups?
According to the introduction to the following paper of Farrell and Jones, if $n>4$ and $\Sigma^n$ is any exotic homotopy sphere, then $T^n\#\Sigma^n$ is not diffeomorphic to $T^n$. So lots of higher- …
- 5,544
9
votes
Accepted
Bott & Tu differential forms Example 10.1
In my version of Bott and Tu, the example reads (emphasis mine):
"Moreover, if $V \subset U$ is an inclusion of CONTRACTIBLE open sets, then $\rho^U_V: H^q(\pi^{-1} U) \to H^q( \pi^{-1} V)$ is an isom …
- 5,544
3
votes
A question on relation of different triangulations of a triangulable space
I'm not completely sure what you're asking, since there are a few things in your question that are unclear. For example, when one talks about chains being homologous, usually the interest is in cycles …
- 5,544
15
votes
Accepted
Any shortcuts to understanding the properties of the Riemannian manifolds which are used in ...
The proof of the existence of good covers is contained in Bott & Tu on pages 42-43, though that proof does refer out to Spivak (see below).
In general, if your main goal is to study (algebraic) topolo …
- 5,544
10
votes
Integral homology classes that can be represented by immersed submanifolds but not embedded ...
I don't know if you'll find this a satisfying example, but what about $2\in \mathbb{Z} \cong H_1(S^1)$? This can be represented by the immersion that wraps the circle twice around itself, but it can't …
- 5,544