Speaker: Rekha Santhanam (JHU)

Title: Equivariant $\Gamma$-spaces and Equivariant $E_\infty$-spaces

Abstract: There are several models of the category of spectra. Segal developed the notion of very-special $\g$-spaces to model connective spectra. May showed that group-like $\E_\infty$-spaces model connective spectra. These can be thought of as combinatorial and algebraic models respectively. May and Thomason showed that these two infinite loop space machines are equivalent.

We describe analogous models of equivariant spectra in the case of finite group actions. We show that the categories of equivariant $E_\infty$-spaces and equivariant $\Gamma$-spaces are Quillen equivalent with appropriate model structures.

We then give a construction of the units of equivariant ring spectra in terms of equivariant $\Gamma$-spaces and show that the units of an equivariant ring spectrum is an equivariant spectrum.