Let $Y \subset X$ be a closed, contractible subspace. Is the collapsing map $$ \pi: X \rightarrow X/Y$$ a homotopy equivalence? If not, what is a counter example?
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2I think this is worth looking at: https://math.stackexchange.com/questions/21705/can-contractible-subspace-be-ignored-collapsed-when-computing-pi-n-or-h-n?rq=1 – SvanN Oct 11 '18 at 15:49
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In particular, Cheerful Parsnip's answer. – Dan Rust Oct 11 '18 at 17:57
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Yes, this is already answered at the previously linked question. – Kevin Carlson Oct 14 '18 at 19:31