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Results tagged with differential-topology
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user 184
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”.
23
votes
0
answers
684
views
Do most manifolds have symmetries? or not?
Let us say that a (closed, connected) manifold has a symmetry if it admits a non-trivial action by a finite group. Note that I am not asking the action to be free. So for example rotating the 2-sphere …
- 27.5k
20
votes
Accepted
Every Manifold Cobordant to a Simply Connected Manifold
Assume that $M^n$ has $\pi_1$ finitely generated (Edit: and n>3). Choose a generator. We will construct (using surgery) a cobordism to $M'$ which kills that generator, and by induction we can kill all …
- 27.5k
18
votes
Accepted
A search for a sequence of $6$-manifolds
I looked at Wall's paper Classification problems in differential topology. V
On certain 6-manifolds. In theorem 3 of that paper Wall describes some invariants of 6-mainfolds, and the relation between …
- 27.5k
11
votes
Accepted
Diffeomorphisms and homotopy equivalences sliced over BO(n)
I wanted to say I think this is a great question, though phrasing things in terms of stacks might scare off some of the people who can best answer this question. I think in general understanding the …
- 27.5k
7
votes
Accepted
Are there 4d state sum models, extended TQFTs or chain mail invariant that detect smooth str...
This MO answer by Arun Debray gives an example in the unoriented case where two specific homeomorphic manifolds can be distinguished by a specific TFT of this kind.
In general all these constructions …
- 27.5k
6
votes
Reference request: gluing manifolds along pieces of boundary
This was a bit too long for a comment, so I am posting it as an answer. You are sort of asking two things:
How to turn your manifolds M and S into an appropriate manifold with corners together with …
- 27.5k
2
votes
Accepted
Relation between Morse Theory and integration against Euler Characteristic
I glanced at the paper briefly. Let me try to explain what I understand. Let us suppose that M is compact and without boundary. Let $f: M \to \mathbb{R}$ be a Morse function. Let us further suppose fo …
- 27.5k
2
votes
Detecting nonorientability
For certain $F$ and $\epsilon_i$ the answer is no. But it is probably yes for generic choices.
Here is an example with n=2 and $M$ the Klein bottle. We start with F being a standard projection of the …
- 27.5k