## EVENT DETAILS AND ABSTRACT

**Topology Seminar**
**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.

**Date:** Monday, March 31, 2014

**Time:** 4:10pm

**Where:** Lunt 104

**Contact Person:** John Francis

**Contact email:** jnkf@math.northwestern.edu

**Contact Phone:** 847-491-5594

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