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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 $\mathbb Q$.
J. GE's user avatar
  • 2,573
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 ...
Michał Kukieła's user avatar
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 ...
gylns's user avatar
  • 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?
gylns's user avatar
  • 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 ...
John Francis's user avatar