Timeline for Involution of 3-sphere
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 13 at 18:36 | comment | added | Anton Petrunin | @IgorBelegradek and IanAgol: the spherical suspension, say $\Sigma^4$ in an Alexandrov space with curvature $\ge 1$ and it is homeomorphic to $\mathbb{S}^4$. It is expected that the fixed point set of codimension 2 in $\Sigma^4$ is an Alexandrov space with curvature $\ge 1$, but it is unknown. If the codimension $\ge 3$ then there are counterexamples. (By the way codimesion 1 case is equivalent to the conjecture that boundary of Alexandrov space is an Alexandrov space.) | |
| May 13 at 18:28 | comment | added | Ian Agol | This is naive, but can you take the spherical warped product and apply the 4D case? | |
| May 13 at 18:26 | comment | added | Igor Belegradek | Why cannot we suspend the involution? Its fixed point set is then the suspension on the given circle. Doesn't an area bound on the 2d suspension gives a bound on the length of the equator? | |
| May 13 at 17:56 | history | asked | Anton Petrunin | CC BY-SA 4.0 |