Timeline for Topology of a Compact Space with Fixed-Point-Free Torus Action
Current License: CC BY-SA 3.0
9 events
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| Jul 15, 2013 at 6:17 | answer | added | Mark Grant | timeline score: 3 | |
| Jul 15, 2013 at 2:18 | comment | added | Peter Crooks | I would like to investigate non-equivariant ways to describe the topology of $X$. Anything about the cohomology of $X$ (or how I might find it) would be welcome, for instance. | |
| Jul 15, 2013 at 2:12 | history | edited | Peter Crooks | CC BY-SA 3.0 |
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| Jul 15, 2013 at 2:11 | comment | added | Peter Crooks | Yes, that's quite right. The cohomology of any manifold can be realized as the equivariant cohomology of a $T$-manifold on which $T$ acts freely. However, I am not particularly interested in $H_T^*(X)$, but in $H^*(X)$. I will amend my question accordingly. | |
| Jul 15, 2013 at 1:35 | comment | added | Jason Starr | What type of result are you looking for? Obviously for every compact, connected, smooth manifold $Q$, taking $X=Q\times T$ with the obvious $T$-action, then $H^*_T(X)$ equals $H^*(Q)$. So, in this sense, there are no further restrictions on $H^*_T(X)$. | |
| Jul 14, 2013 at 22:38 | history | edited | Peter Crooks | CC BY-SA 3.0 |
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| Jul 14, 2013 at 19:28 | history | edited | Peter Crooks | CC BY-SA 3.0 |
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| Jul 14, 2013 at 19:16 | history | edited | Peter Crooks | CC BY-SA 3.0 |
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| Jul 14, 2013 at 19:10 | history | asked | Peter Crooks | CC BY-SA 3.0 |