Timeline for Genuine equivariant ambidexterity

6 events

when toggle format	what		by	license	comment
Jan 16, 2016 at 20:43	comment	added	Yonatan Harpaz		Do you mean that if $G$ is finite and one works in the $K(n)$-local setting then the genuine fixed point construction is both left adjoint and right adjoint to the constant-genuine-action functor? (I suppose in this case it will be a form of ambidexterity, although of a somewhat confusing nature, as the left adjoint did not exist a-priori)->(in this case I might also reraise my original question, suggesting it could work for all compact lie groups)
Jan 16, 2016 at 19:51	comment	added	Jacob Lurie		That's another way to describe the problem. The genuine fixed point construction is right adjoint to a functor from spectra to $G$-spectra, given informally by "let $G$ act trivially". But the "trivial action" functor doesn't preserve homotopy limits, and therefore doesn't have a left adjoint. (Though if you work in the $K(n)$-local setting and $G$ is finite, then this issue goes away: the right adjoint will also be a left adjoint.)
Jan 16, 2016 at 19:48	vote	accept	Yonatan Harpaz
Jan 16, 2016 at 19:41	comment	added	Yonatan Harpaz		Thanks! So basically not only is it not ambidextrous, it doesn't even have two hands.
Jan 16, 2016 at 19:27	history	edited	Jacob Lurie	CC BY-SA 3.0	deleted 1 character in body
Jan 16, 2016 at 19:18	history	answered	Jacob Lurie	CC BY-SA 3.0