Transfer in generalized prestack cohomology

Abstract

The purpose of this paper is to define cohomology with coefficients in a local system of simplicial spectra and show this leads to a simple definition of the transfer homomorphism for a finite covering map. We wish to point out that the method of constructing the transer map in §3 of this paper gives a different approach to the one developed by F. W. Roush in his thesis. 1. Preliminaries. In this section we define those categories and functors of special interest. We assume the reader is familiar with the theory of simplicial sets and spectra as presented in [7], [9], [8], [4], and [3], We let £?(£?*) be the category of simplicial sets (pointed simplicial sets) equipped with its standard closed model structure. Similarly we let S/fι {^^ψ) be the category of simplicial spectra (group spectra) equipped with its standard closed model structure as defined in [3, Thm. 5, Pg. 439]. For X e Sf (E e 2ft) we let Xp (Ep) be the set of /?-simplexes of X