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Results tagged with differential-topology
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user 11142
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”.
6
votes
Accepted
Computing the Euler characteristic of the complex projective plane using differential topology
There is a canonical way to construct holomorphic vector fields on $\mathbb{C}P^2,$ and that way is described in Zoladek's "Monodromy Group", page 335. If you read the description, it will be pretty c …
- 96.4k
5
votes
Computing the Euler characteristic of the complex projective plane using differential topology
By the way, a very cool (to my mind) way of computing the Euler characteristic of $\mathbb{C}P^n$ is to treat it as the $n$-fold symmetric product of $\mathbb{C}P^1 = \mathbb{S}^2$ with itself. Then, …
- 96.4k
1
vote
on product of some spaces
This question (or a close relative) is discussed and answered in
When factors may be cancelled in homeomorphic products?
- 96.4k
4
votes
Extension of a group action beyond the boundary
If you are asking for a topological action, then it would seem you can just double $M$ along the boundary. I am not sure this works in the smooth category..
- 96.4k
3
votes
18
votes
Homeomorphisms of $S^n\times S^1$
This is false for $n=1.$ The mapping class group of the torus is $SL(2, Z),$ of which the homeomorphisms you describe are but a small part - the parabolic matrices $\begin{pmatrix}1 & n\\ 0 &1\end{pma …
- 96.4k
3
votes
Structural stability on the circle
You can read Jaco Palis' PhD thesis. The result is presumably also in deMelo/vanStrien
http://w3.impa.br/~demelo/tablecon.html
EDIT
Here is the link to the published version of Palis's thesis:
http:// …
- 96.4k
9
votes
Extending a diffeomorphism of the sphere $S^2$ to the ball $D^3$
A combinatorial proof of Smale's theorem (actually a stronger theorem, which at the time of the paper cited was a conjecture of N. Kuiper) is given in the paper
The space of simplexwise linear homeom …
- 96.4k
6
votes
Obstruction to a general S^1-action
It is a result of Atiyah-Hirzebruch (1970) that the $\hat{A}$ genus of a spin manifold with a nontrivial $S^1$ action vanishes, and a result of Herrera and Herrera that the same result, if the manifo …
- 96.4k
4
votes
Accepted
Set of density matrices
This is a symmetric space when equipped by the metric discussed in this question (it is Riemannian, when $p=2$). The metric is clearly invariant under the action; its other properties can be checked ( …
- 96.4k
0
votes
When a homeomorphism is a diffeomorphism w.r.t to a suitable smooth structure?
Just a slight addition to Danny Ruberman's answer: more example in the same vein are discussed in David Gay's note "4-manifolds which are homeomorphic but not diffeomorphic".
- 96.4k
11
votes
Accepted
is there a diffeomorphism with only finite orbits but of infinite order?
No, there is no such animal. This is due to Montgomery (1938), see my answer to this question: Nonperiodic points of homeomorphisms of a ball
- 96.4k
4
votes
Diffeomorphisms of a surface in terms of generators.
If your question is: can you present the homeotopy group in terms of generators and relations, the answer is "yes", following the work of Hatcher-Thurston, Wajnryb, and most recently M. Korkmaz, who g …
- 96.4k
10
votes
Accepted
Is a compact, connected, orientable 3-manifold with $\mathbb{Z}^K$ fundemental group uniquel...
NO, since the three-torus $T^3$ does not have this form.
EDIT if the OP really means a free product of $\mathbb{Z}$s, so the free group $F_k,$ then the answer is YES. It is a fact (see Hempel's book, …
- 96.4k
2
votes
Reference request: gluing manifolds along pieces of boundary
This seems to be discussed here. (particularly page 6)
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