most recent 30 from http://mathoverflow.net 2013-05-26T08:35:21Z http://mathoverflow.net/feeds/question/25194 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/25194/equivariant-sheaves-of-equivariant-spectra Dan 2010-05-19T01:11:00Z 2010-05-19T01:11:00Z

<p>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? </p> <p>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)?</p> <p>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? </p>