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Homotopy theory, homological algebra, algebraic treatments of manifolds.
3
votes
1
answer
273
views
Topology of functional spaces
Let $X$ be a finite CW-complex of dimension $n$. Fix an natural number $k < n$, and let $M(X, \mathbb{S}^k)$ be the space of all continuous function from $X$ to the k-sphere $\mathbb{S}^k$ endowed wi …
4
votes
1
answer
251
views
Homotopy type of G-CW-structure
Let $G$ be a finite group, and $X$ be a free $G$-space. Moreover, assume that $X$ has a homotopy type of a CW-complex. Does $X$ have $G$-homotopy type of a $G$-CW complex also?
Edit: My main motivati …