2
votes
0answers
217 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 ...
5
votes
0answers
188 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 ...
3
votes
1answer
199 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 ...
4
votes
1answer
686 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 $\le n$?
4
votes
3answers
485 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 ...
1
vote
0answers
986 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 ...
2
votes
1answer
2k 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?
20
votes
6answers
2k 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 ...