Timeline for Does positive scalar curvature imply vanishing of the simplicial volume on a closed Riemannian manifold?
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 1, 2020 at 3:56 | vote | accept | Jialong Deng | ||
| Nov 14, 2019 at 1:24 | answer | added | Paul Siegel | timeline score: 8 | |
| Oct 22, 2019 at 9:39 | comment | added | Grisha Papayanov | @ThomasRichard Product of anything with a sphere have vanishing simplicial volume (since such a space admits a self-map of positive degree), and in dimensions more than two simplicial volume is additive with respect to connected sum, so for these examples volume is zero. | |
| Oct 22, 2019 at 9:36 | comment | added | Thomas Richard | Does anyone knows the simplicial volume of the connected sum of two copies of $\mathbb{S}^{n-1}\times\mathbb{S}^1$ ? It does have metric with positive scalar curvature thanks to the construction of Gromow and Lawson but its $\pi_1$ has exponential growth, that would be a good test case, as are product $M\times\mathbb{S}^2$. | |
| Oct 22, 2019 at 9:23 | comment | added | Grisha Papayanov | I am dumb and read "sectional" instead of "scalar". Should get more sleep. | |
| Oct 22, 2019 at 9:18 | comment | added | Jialong Deng | @Grisha, any closed manifold times with 2-sphere admits metrics with positive scalar curvature. | |
| Oct 22, 2019 at 9:15 | answer | added | Grisha Papayanov | timeline score: 1 | |
| Oct 22, 2019 at 9:09 | comment | added | Grisha Papayanov | If scalar curvature is bounded from below by a positive number, then $\pi_1$ is finite and so simplicial volume is zero | |
| Oct 22, 2019 at 8:29 | history | asked | Jialong Deng | CC BY-SA 4.0 |