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Results tagged with cw-complexes
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user 184
12
votes
Is any CW complex with only finitely many nonzero homology groups homotopic to a finite dime...
As requested I am writing this as an answer.
No there are spaces with vanished homology which are not homotopy equivalent to finite CW-complexes.
For example if $G$ is an acyclic group, then the cl …
- 27.5k
11
votes
What does actually being a CW-complex provide in algebraic topology?
Here is another interesting class to throw in the mix in between CW-complexes and general spaces. They are defined exactly like CW-complexes, by inductively attaching cells, except that you are allow …
- 27.5k