All Questions
Tagged with examples gt.geometric-topology
16
questions
13
votes
1
answer
541
views
Is there an orientable prime manifold covered by a non-prime manifold?
A manifold is called prime if whenever it is homeomorphic to a connected sum, one of the two factors is homeomorphic to a sphere.
Is there an example of a finite covering $\pi : N \to M$ of closed ...
- 18.5k
15
votes
1
answer
1k
views
Examples of hyperbolic groups
What are some other classes of word-hyperbolic groups other than the finite groups, fundamental groups of surfaces with Euler characteristics negative and virtually free groups?
- 305
3
votes
1
answer
300
views
Simply connected 4-manifolds with boundary
I think I've encountered a question about 4-manifolds which maybe easy but I'm not familiar with. Can anyone give me an example of a simply connected 4-manifold $M$ (with boundary, of course) with $...
- 123
19
votes
1
answer
747
views
Vector field on a K3 surface with 24 zeroes
In https://mathoverflow.net/a/44885/4177, Tilman points out that one can use a $K3$ surface minus the zeroes of a generic vector field to build a nullcobordism for $24[SU(2)]$. Given that a) this is a ...
- 33.2k
6
votes
1
answer
1k
views
Example of a triangulable topological manifold which does not admit a PL structure
I know there are some examples of manifolds which don't admit a PL structure (combinatorial triangulation), and that it has been recently proven that in dimension $n\geq5$ there are manifold which are ...
- 643
6
votes
5
answers
762
views
Existence of orientation preserving, finite order self homeomorphism on a genus 2 surface without fixed point
Let $M$ be a compact 2-manifold of genus 2. Does there exist an orientation preserving homeomorphism $f:M\to M$, so that $f^n=id$ for some integer $n$, and $f$ doesn't have fixed points?
Using ...
- 947
3
votes
0
answers
493
views
Closed 4-manifolds with uncountably many differentiable structures
I know that $\mathbb{R}^4$ admits uncountably many differentiable structures and I was wandering what happen if we consider closed 4-manifolds. Are there any closed 4-manifolds with uncountably many ...
- 643
6
votes
0
answers
740
views
Homeomorphisms of product spaces: an example
In the first of these lectures (http://www.mpim-bonn.mpg.de/node/4436) given by M. Freedman he says that there exists (compact metric) spaces $X$ and $Y$ such that $X\times S^{1}$ is homeomorphic to $...
- 643
28
votes
1
answer
2k
views
Example of 4-manifold with $\pi_1=\mathbb Q$
This might be well known for algebraic topologist. So I am looking for an explicit example of a 4 dimensional manifold with fundamental group isomorphic to the rationals $\mathbb Q$.
- 2,573
6
votes
1
answer
451
views
Satellite knot example
Can someone provide me with an example of a satellite knot with symmetry group which is neither cyclic nor dihedral?
- 61
3
votes
1
answer
443
views
When is the Freudenthal compactification an ANR?
Let $X$ be a locally compact metric ANR (or, if preferred, a locally compact simplicial complex). If needed, assume that $X$ has finitely many ends or is of finite dimension. My question is:
What are ...
- 2,064
4
votes
1
answer
774
views
Example in dimension theory
Could you give me an example of a complete metric space wiht covering dimension $> n$ all of which compact subsets have covering dimension $\le n$?
- 1,785
5
votes
3
answers
564
views
Natural examples of finite dimensional spaces with interesting 2-type
Riemann surfaces provide interesting examples of 1-types - interesting as they have roles in diverse areas. However, apart from 2-dimensional lens spaces, I can't readily bring to mind natural ...
- 33.2k
1
vote
0
answers
1k
views
Again about Bing's house with two rooms [duplicate]
Possible Duplicate:
How to show that the “bing’s house with two rooms” is contractible?
I don't know why my question is closed? here, I make my question clearly, when "hollowing ...
- 187
3
votes
1
answer
4k
views
How to show that the "bing's house with two rooms" is contractible? [closed]
I can't image this, Someone can give a clear illustration?
- 187
27
votes
6
answers
4k
views
Failure of smoothing theory for topological 4-manifolds
Smoothing theory fails for topological 4-manifolds, in that a smooth structure on a topological 4-manifold $M$ is not equivalent to a vector bundle structure on the tangent microbundle of $M$. Is ...
- 947