Timeline for Is the localised $S^1$-equivariant cohomology of the free loop space of a space $X$ isomorphic to that of $X$ itself?
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 10, 2023 at 10:45 | vote | accept | Eugenio Landi | ||
| Feb 23, 2023 at 11:52 | vote | accept | Eugenio Landi | ||
| Feb 23, 2023 at 17:38 | |||||
| Feb 22, 2023 at 7:27 | comment | added | domenico fiorenza | This is quite interesting but also rather surprising: an isomorphism $i^*:H^*_{S^1}(LM;\mathbb{Q}))_{(u)}\to H^*_{S^1}(M;\mathbb{Q})_{(u)}=H^*_{per}(M;\mathbb{Q})$ would have nicely fit into the factorization of the Chern character isomorphism $Ch: K^0(M)\otimes\mathbb{Q}\xrightarrow{\sim} H^0_{per}(M;\mathbb{Q})$ into the composition of the Bismut-Chern character $BCh:K^0(M)\otimes\mathbb{Q}\to H^0_{S^1}(LM;\mathbb{Q}))_{(u)}$ and the restriction to fixed points $i^*$. Clearly no need that $BCh$ and $i^*$ are isomorphism for $Ch$ to be, but it would have been nice. | |
| Feb 22, 2023 at 0:57 | history | answered | Tom Goodwillie | CC BY-SA 4.0 |