Timeline for Spaces with same homotopy and homology groups that are not homotopy equivalent?
Current License: CC BY-SA 2.5
10 events
| when toggle format | what | by | license | comment | |
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Jan 27, 2011 at 13:18 | comment | added | Steven Sivek | It's the last comment on my answer here: mathoverflow.net/questions/3540/… | |
| Jan 27, 2011 at 7:05 | comment | added | Dylan Thurston | $L(5,1)$ and $L(5,2)$ are an excellent example, although I didn't see them at any link. | |
| Jan 27, 2011 at 7:01 | vote | accept | Dylan Thurston | ||
| Jan 26, 2011 at 21:52 | answer | added | Somnath Basu | timeline score: 38 | |
| Jan 26, 2011 at 21:39 | comment | added | Steven Sivek | Since the homology groups of a closed 3-manifold are determined by the fundamental group, any pair of non-homotopy-equivalent 3-manifolds with the same homotopy groups should work, like the lens spaces L(5,1) and L(5,2) I mentioned in a comment at the above link. | |
| Jan 26, 2011 at 21:31 | answer | added | Johannes Ebert | timeline score: 15 | |
| Jan 26, 2011 at 21:29 | answer | added | Ben Wieland | timeline score: 10 | |
| Jan 26, 2011 at 21:25 | comment | added | John Klein | It seems to me that Allen Hatcher's examples in mathoverflow.net/questions/4665/… gives what you want. These are total spaces of spherical fibrations over spheres. The simplest examples I think are $S^3 \times S^3$ and the total space of the fibration $S^3 \to E\to S^3$ given by the unit sphere bundle of the Hopf bundle plus the trivial bundle. | |
| Jan 26, 2011 at 20:32 | history | asked | Dylan Thurston | CC BY-SA 2.5 |