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Results tagged with dg.differential-geometry
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user 75
Complex, contact, Riemannian, pseudo-Riemannian and Finsler geometry, relativity, gauge theory, global analysis.
3
votes
Accepted
Are maps homotopic with respect to a uniform number of local homotopies
Yes, you can always connect $f_0$ and $f_1$ by a finite sequence of good homotopies supported in any given open cover (and in fact, this sequence of good homotopies can be chosen to be homotopic to $f …
- 31.2k
58
votes
Cohomology and fundamental classes
This is a reply to Alon's comment, but it's too long to be a comment and is probably interesting enough to be an answer.
Here's an example Thom gives of a homology class that is not realized by a subm …
- 31.2k
17
votes
Spectrum of Ring of Smooth Functions on $\mathbb{R}^n$
A trivial way you can tell this is false is that Spec of any ring is (quasi)compact, but $\mathbb{R}^n$ is not (if $n>0$).
A bit less trivially, this is still false if you replace $\mathbb{R}^n$ with …
- 31.2k
9
votes
(how) are vector bundles and homotopy groups related?
You have it backward--vector bundles on X are the same as homotopy classes of maps from X to an infinite-dimensional Grassmannian, with the correspondence being given by pulling back the tautological …
- 31.2k