Subject: question for the list
From: Tom Goodwillie
Date: Wed, 28 Feb 2007 01:02:22 -0500
I have a reference question about stable equivariant homotopy theory. It's
about the relationship between "fixed points" and "geometric fixed points"
for a G-spectrum.
Let G be a finite group and X a G-spectrum.
The thing called "geometric fixed point spectrum" can be defined in a
couple of ways. One of them is "smash X with a certain G-CW complex \tilde
EG and then take fixed points". That based G-space E =\tilde EG can be
characterized by the statement that for every proper subgroup H the fixed
point set E^H is contractible while E^G~S0.
In the case of a group of prime order this leads to the statement that
there is a homotopy (co)fibration sequence of spectra
(homotopy orbits) --> (fixed points) --> (geometric fixed points)
My question is, what is a good generalization of this to general finite G,
and where is a good place to read about it? I can sort of see how one such
answer goes, but I'd rather not be reinventing the wheel.
Tom Goodwillie