Timeline for Homotopy group action and equivariant cohomology theories
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 18 at 1:36 | comment | added | Dmitri Pavlov | @JackDavidson: Dwyer–Kan, Equivalences between homotopy theories of diagrams, Theorem 2.4. | |
| Jan 17 at 16:27 | comment | added | JD1874 | @DmitriPavlov which paper of Dwyer and Kan is this? Unfortunately, the 80s does not narrow it down too much for them two! | |
| Jul 3, 2020 at 11:35 | vote | accept | Arkadij | ||
| Jul 3, 2020 at 9:59 | answer | added | Lennart Meier | timeline score: 5 | |
| Jul 2, 2020 at 23:41 | answer | added | David White | timeline score: 2 | |
| Jul 2, 2020 at 23:11 | history | edited | David White | CC BY-SA 4.0 |
added 1 character in body
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| Jul 2, 2020 at 2:22 | history | became hot network question | |||
| Jul 1, 2020 at 23:20 | comment | added | Dmitri Pavlov | As shown by Dwyer and Kan in 1980s, any homotopy coherent ∞-group action can be strictified to a strict action of a simplicial group on a simplicial set, or a topological group on a topological space. So passing to the homotopy coherent setting yields nothing new. As already observed in other comments, for Bredon equivariance one really needs presheaves on the orbit category. | |
| Jul 1, 2020 at 20:01 | comment | added | mme | It's just me being lazy in notation. It's a bar construction $B(G,G,X)$, which makes sense in the coherent setting. | |
| Jul 1, 2020 at 19:12 | comment | added | Arkadij | What does $EG\times_G X$ mean in this case? The diagonal "action" won't give me a relations as it isn't really an action. Is it just notation? | |
| Jul 1, 2020 at 18:46 | answer | added | S. carmeli | timeline score: 8 | |
| Jul 1, 2020 at 18:31 | comment | added | mme | The right notion of homotopy coherent $G$-space to recover Bredon equivariant cohomology is not obvious to me, but it's probably encoded as some fibering over the orbit category. I'm sure an expert will arrive shortly to explain the right notion. | |
| Jul 1, 2020 at 18:30 | comment | added | mme | A homotopy coherent group action is only enough to reconstruct Borel cohomology theories, because it is not enough to describe how the "fixed point spaces" should interact for various subgroups $H \subset G$. A homotopy coherent group action may be strictified in the sense that there will be a space $EG \times_G X$ with strict $G$-action and a continuous (coherently equivariant) map $EG \times_G X \to X$ which is a nonequivariant homotopy equivalence. | |
| Jul 1, 2020 at 18:00 | history | asked | Arkadij | CC BY-SA 4.0 |