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Results tagged with cw-complexes
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user 23571
79
votes
Accepted
Maps which induce the same homomorphism on homotopy and homology groups are homotopic
Take the composition of a degree one map $f:T^3\to S^3$ with the Hopf map $g:S^3\to S^2$, where $T^3$ is the 3-torus. This composition is trivial on homotopy groups since $T^3$ is aspherical and $\pi_ …
- 20k
28
votes
Accepted
Is the space of diffeomorphisms homotopy equivalent to a CW-complex?
Here is an example where ${\rm Diff}(M)$ with the compact-open topology is not homotopy equivalent to a CW complex. Take $M$ to be a surface of infinite genus, say the simplest one with just one nonco …
- 20k
13
votes
Accepted
How can I endow a "locally product" CW structure on a vector bundle over a CW complex?
The authors of this book are attempting to use CW structures to justify certain cohomology isomorphisms, but this seems to be the wrong approach since some of their claims about CW structures are just …
- 20k
4
votes
Accepted
Relationship between quotient CW-complexes after attaching cells
If I understand the question correctly, you have a CW complex $Y'$ which is the union of two subcomplexes $Y$ and $X'$ whose intersection is the subcomplex $X$. We can first collapse $X$ to a point t …
- 20k