All Questions
15 questions with no upvoted or accepted answers
14
votes
0
answers
312
views
An unpublished paper of Thurston about diffeomorphism groups
William Thurston has done many contributions in the field of diffeomorphism groups. But it seems that one of his papers entitled
"On the Structure of the Group of Volume Preserving Diffeomorphisms"
...
- 747
5
votes
0
answers
289
views
A certain kind of proof of the Hairy Ball Theorem
I'd just like to know if proofs of the Hairy Ball Theorem along the following lines are well-known or even somewhere in the literature.
From a given vector field $V_1$ on $S^2$, form another, $V_2$, ...
- 17.6k
5
votes
0
answers
261
views
The space of $k$ differential forms as a Fréchet space
Given a smooth manifold $M$, can define define seminorms on $\Gamma(U,\bigwedge^kT^{\ast}M)$ for $U$ a coordinate open set by the following: $p^{s}_L(u = \sum_{I}u_I dx_I) = \sup_{x \in M}\max_{|I|=p, ...
- 51
5
votes
0
answers
1k
views
Prerequisites for reading Gregory Perelman's work
What are the prerequisites for understanding the work of Perelman concerning the Poincaré conjecture?
I am referring to the last three papers here.
- 1,594
4
votes
0
answers
116
views
Do any Legendrian knots in standard contact 3-space have big tubular neighborhoods?
Consider $\mathbb{R}^3$ with the standard contact structure $\ker(dz-y\,dx)$.
According to the contact version of Weinstein's theorem, any Legendrian knot $L\subset \mathbb{R}^3$ has a tubular ...
- 491
4
votes
0
answers
343
views
Riemannian metrics on a manifold with corners
For a smooth manifold with corners (although maybe there is no universally agreed definition of it), is there always a Riemannian metric making every face totally geodesic?
Is there any reference ...
- 803
4
votes
0
answers
162
views
Question about density of $C^{\infty}(M,N)$ in $W^{1,p}(M,N)$ with $N$ not compact
Hi!
Let $M$ be a compact manifold possibly with boundary with $\dim(M)=m$, let $N$ be a non compact manifold with $\dim(N)=n$. Let me recall the definition of the sobolev space $W^{1,p}(M,N)$. ...
- 1,727
3
votes
0
answers
74
views
Deforming a non-positively curved Riemannian manifold into a negatively curved one
Cheeger deformations can be used to deform some non-negatively curved Riemannian manifolds into positively curved manifolds (e.g., sectional curvatures strictly positve), see
What is a Cheeger ...
- 1,942
2
votes
0
answers
344
views
If the fibers of a submersion are connected, does it mean that any 2 sections are homotopic (locally on the base)?
Is the following fact known? If yes - what is the reference?
Let $\phi:X\to Y$ be a submersion of smooth manifolds with connected fibers.
Let $s_0,s_1:Y\to X$ be its (smooth) sections. Then, for any $...
- 2,639
2
votes
0
answers
260
views
Perturbation of Morse function at a critical point
I recently learned from a knowledgeable person that for a Morse function $f: M \to R$ with a critical point $x_0$, one can perturb $f$ in such a fashion that the new function has the same critical ...
- 1,211
1
vote
0
answers
170
views
Uniqueness of collar neighborhoods for non-compact boundary case in smooth setting
Let $M$ be a smooth manifold and let $f_0, f_1 \colon [0, 1] \times
\partial M \to M$ be two smooth embeddings that are the identity map
on $\partial M \times\{0\} = \partial M$ . If $\partial M$ is
...
- 265
1
vote
0
answers
55
views
Projection of a real analytic manifold onto subspace is union of real analytic submanifolds
Let $M$ be a compact connected real analytic submanifold of the Euclidean space $\mathbb{R}^{n} \times \mathbb{R}$ and denote by $\pi : \mathbb{R}^{n} \times \mathbb{R} \rightarrow \mathbb{R}^{n}$ the ...
- 19
1
vote
0
answers
61
views
Splitting formulas for spectral flows
I'm asking if there are splitting formulas for equivariant spectral flow and higher spectral flow (of Dai-Zhang) for paths of Dirac operators, concerning gluing together two smooth compact Spinc ...
- 11
1
vote
0
answers
126
views
Flows commuting with Anosov flows and further reference request
Hello respected members of Mathoverflow. I was reading the paper "Flots d’Anosov dont les feuilletages stables sont différentiables" by Etienne Ghys and there was a statement which he remarked was ...
- 229
1
vote
0
answers
119
views
Orbits and indices of vector fields
I'm afraid this might be an exercise in differential topology (in which case a reference to a book where it is would be very much appreciated); apologies in advance. Given an analytic vector field (in ...
- 4,432