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Results tagged with at.algebraic-topology
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user 4344
Homotopy theory, homological algebra, algebraic treatments of manifolds.
4
votes
How to tell whether a compact manifold can be realized as a nontrivial fiber bundle?
As I commented above, if you do not impose the condition that the fiber $F$ be connected, it might be difficult to answer the question. On the other hand, there is something that you can use assuming …
- 5,137
3
votes
X not simply connected and X-x contractible
(This should have been a comment to Andreas Blass' answer, but it did not fit there.) To answer the stronger question, asked in a comment to Andreas Blass' answer you can argue as follows in the case …
- 5,137
5
votes
Small simplicial complexes with torsion in their homology?
You might be able to do slightly better than with David's construction, but still with a number of vertices linear in $p$. Namely, you present the group $\mathbb{Z}/p\mathbb{Z}$ by a single generator …
- 5,137
7
votes
Ring of closed manifolds modulo fiber bundles
The ring $R$ is graded by dimension, and it is trivial in dimension one, by the observation in the question. In dimension two, the connected orientable surfaces of genus at least two are all topologic …
- 5,137
5
votes
The topological analog of flatness?
An immediate comment is that, in the case of smooth manifolds, the notion that you suggest needs to take into account more than just the differentiable structure of $X$ and $Y$: any two smooth, connec …
- 5,137