Timeline for What's with equivariant homotopy theory over a compact Lie group?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Sep 3, 2017 at 14:10 | comment | added | Tyler Lawson | @TimCampion When $n = \infty$ you're right, there's the norm-restriction adjunction for genuine $S^1$-equivariant rings. | |
| Sep 2, 2017 at 22:51 | comment | added | Tim Campion | @DavidWhite the part of the weirdness they describe that I'm able to follow is that in their setup, it seems the orbit category is still the category of finite G-sets, which just looks like a shortcoming of their setup to me, not a fundamental difficulty. Are they saying more than that? | |
| Sep 1, 2017 at 13:42 | comment | added | David White | Have you seen this 2016 preprint of Hill and Hopkins? arxiv.org/abs/1610.03114. In section 8 they give some strange things that can happen with compact Lie groups but don't happen with finite groups. It's all about pointing out how our intuition can fail us. | |
| Sep 1, 2017 at 6:54 | comment | added | Tim Campion | @TylerLawson Oh, I suppose I had it in my head that for an $E_\infty$ ring spectrum $A$, $THH_A: E_n\operatorname{-Alg}(A) \to E_{n-1}\operatorname{-Alg}(A)_{S^1}$ should simply be left adjoint to a forgetful functor -- but at least when $n \neq \infty$ I'm now realizing that it's not even clear what this forgetful functor should be. Is this at least one of the options? | |
| Sep 1, 2017 at 4:37 | comment | added | Tyler Lawson | Regarding (5), a problem with THH is that the genuine $S^1$-fixed point set depends on the model we use for THH and there appears to be no "intrinsic" definition. There are models for which this fixed-point set is actually algebraic K-theory. | |
| Sep 1, 2017 at 4:31 | answer | added | Marc Hoyois | timeline score: 14 | |
| Sep 1, 2017 at 4:07 | comment | added | Harry Gindi | Curious about this as well | |
| Sep 1, 2017 at 2:12 | history | asked | Tim Campion | CC BY-SA 3.0 |