Timeline for If M times circle admits a locally CAT(0)-metric, then M also carries a locally CAT(0)-metric?
Current License: CC BY-SA 4.0
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| Apr 13, 2023 at 19:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Dec 14, 2022 at 18:05 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Nov 15, 2022 at 20:51 | comment | added | Anton Petrunin | + If $M\times \mathbb{S}^1$ is a torus, then the answer is yes, but it is not trivial; see mathoverflow.net/questions/403202 | |
| Nov 14, 2022 at 11:56 | answer | added | Anton Petrunin | timeline score: 1 | |
| Nov 12, 2022 at 16:12 | comment | added | Anton Petrunin | It seems that I can show that $M\times \mathbb{S}^1$ splits isometrically, but it does not imply the existence of a CAT(0)-metric on $M$ --- we only get a CAT(0)-metric on a manifold $M'$ that is bordant to $M$. | |
| Nov 11, 2022 at 17:07 | history | edited | Anton Petrunin |
edited tags
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| Jul 30, 2019 at 20:48 | comment | added | Igor Belegradek | A suggestion: There should be a version of the splitting theorem for groups with infinite center. For Riemannian locally CAT(0) metrics it can be found in Schroeder's Inventiones splitting theorem paper. In this version the universal cover of a closed nonpositively curved manifold with $\pi_1\cong H_1\times H_2$ splits as the product of three factors $X_0\times X_1\times X_2$ where $X_0$ is Euclidean and each $H_i$ acts trivially on $X_{3-i}$ and by translation on $X_0$. Try to deform the $H_i$-action to the trivial one through translations by keeping $H_1\times H_2$ discrete. | |
| Jul 30, 2019 at 19:54 | history | edited | YCor | CC BY-SA 4.0 |
fixed English, formatting
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| Jul 30, 2019 at 18:27 | history | asked | Jialong Deng | CC BY-SA 4.0 |