All Questions
13 questions with no upvoted or accepted answers
21
votes
0
answers
777
views
Is the mapping class group of $\Bbb{CP}^n$ known?
In his paper "Concordance spaces, higher simple homotopy theory, and applications", Hatcher calcuates the smooth, PL, and topological mapping class groups of the $n$-torus $T^n$. This requires an ...
- 9,580
16
votes
0
answers
438
views
Survey of known results on equivariant transversality
Most basic differential topology theorems carry over to the equivariant case with mild modifications; see for instance Wasserman's paper. One thing that fails (more or less obviously) is equivariant ...
- 9,580
7
votes
0
answers
448
views
Reference Request: Topological h-cobordism theorem in higher dimensions
I think this question on math.stackexchange is more appropriate on mathoverflow. Correct me, if you don't think so.
The h-cobordism theorem is true in the topological and in the smooth category in ...
- 71
7
votes
0
answers
208
views
How do metrics behave under joining along a manifold embedded in the boundary?
How do metrics behave under joining along a manifold embedded in the boundary?
This is, more-or-less, part of Problem 4.66 in Kirby's List:
Problem 4.66 How do metrics (e.g. Riemannian, Lorentz, ...
- 1,897
6
votes
0
answers
321
views
Elementary questions about Morse-Bott functions
Let $M$ be a manifold, $F$ be a Morse-Bott function, $c$ be a critical level, and $M_c$ be the corresponding critical submanifold. Let us assume that $M_c$ is connected, and the index of $M_c$ is ...
- 14.3k
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
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
5
votes
0
answers
461
views
When does a manifold 'deformation retract' into a small neighborhood of some k-dimensional subpolyhedron?
Under which conditions does a m-manifold $M^m$ admit a deformation retraction to a
small neighborhood of some k-dimensional subpolyhedron?
Or, under which conditions is the identity map $id_M$ of a ...
- 722
3
votes
0
answers
228
views
Diffeomorphism classification of Grassmannian manifolds
Is anything known about the diffeomorphism classification of Grassmannian manifolds? I know that there are some results on projective spaces (for example in Lopez de Medrano's "Involutions on ...
- 93
2
votes
0
answers
146
views
Explicit S-duality map
$\DeclareMathOperator{\Th}{Th}$
The Thom space of a closed manifold $M$ ($\Th(M)$) is the $S$-dual to $M_+ (=M \cup \{pt\})$. Let $M$ be embedded in $\mathbf R^{n+k}$. I found the duality map from $S^...
2
votes
0
answers
543
views
Tubular neighbourhoods are unique up to ambient isotopy?
Let $M$ be a closed smooth submanifold of $N$. It is well known that tubular neigbourhoods of $M$ are diffeomorphic to the normal bundle of $M$ in $N$ and therefore to each other. Are they smoothly ...
- 313
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
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