MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

This is a very naive question but 1)given a compact Lie group G, is there a good notion of a sheaf of equivariant spectra on a G-space X analogous to the model structure that Brown develops in his paper on ordinary sheaves of spectra?

2)Is there a homotopy theory which allows you to take cohomology with coefficients in a sheaf of spectra and in which it makes sense to take for a G-space X the constant sheaf Z and recover Borel cohomology or "the constant sheaf in the equivariant K-theory spectrum" and recover K_G(X)?

3) Assuming answers to the previous questions, does the picture simplify in a reasonable way when one works rationally by analogy with the usual rational homotopy theory?

share|cite|improve this question
This sounds somewhat close to twisted cohomology, where one takes the sheaf of sections of a bundle of spectra. You might look at some of the literature on twisted K-theory (and in particular, twisted K-theory of stacks, which is essentially an equivariant version). – Jeffrey Giansiracusa May 19 '10 at 10:16

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.