Timeline for Homotopy equivalent cartesian product of closed manifold
Current License: CC BY-SA 4.0
6 events
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| Jul 31, 2021 at 20:36 | comment | added | Michael Albanese | You can even take $M\times S$ diffeomorphic to $N\times S$ (i.e. $S' = S$), and the conclusion is false. In particular, you need not even have $\pi_1(M) \cong \pi_1(N)$, see here for example. | |
| Jul 31, 2021 at 20:29 | history | edited | Paris | CC BY-SA 4.0 |
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| Jul 31, 2021 at 19:40 | comment | added | skupers | Theorem 2 of sciencedirect.com/science/article/pii/0040938378900149 provides a counterexample with $S = S'$ a 3-sphere and $M$, $N$ lens spaces. | |
| Jul 31, 2021 at 19:10 | comment | added | mme | I certainly can't imagine what your argument would be; I doubt that the result is true. I would try to take M, N inequivalent lens spaces and see if I can find an example with S = S' in the literature. | |
| Jul 31, 2021 at 18:41 | history | edited | Paris | CC BY-SA 4.0 |
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| Jul 31, 2021 at 18:26 | history | asked | Paris | CC BY-SA 4.0 |