EVENT DETAILS AND ABSTRACT

Title: Equivariant Diagrams and Equivariant Excision
Speaker: Emanuele Dotto
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

In a non-equivariant setting, a functor is excisive if it takes homotopy pushout squares to homotopy pullback squares. Given a finite group G and a functor from G-spaces to G-spaces (or G-spectra), this definition of excision does not "capture enough equivariancy". For example the category of endofunctors of G-spaces with this property does not model G-spectra. One solution is to replace squares by "cubes with action", where the group is allowed to act on the whole diagram by permuting its vertices. I will talk about the homotopy theory of these equivariant diagrams and relate the resulting notion of equivariant excision to previous work of Blumberg. As an application of this theory, I will give a proof of the Wirthmuller isomorphism that uses only the equivariant suspension theorem and formal manipulations of limits and colimits.