Introduction to stable equivariant homotopy theory

Date: 2022-06-07

Time: 11:00 - 12:00

Zoom link:


Clover May


Equivariant stable homotopy theory for a finite group G is complicated (in part) by the many flavors of spheres. Their presence leads us to work with richer algebraic structures than we encounter non-equivariantly. For example, instead of the usual homotopy abelian groups, we naturally have the structure of homotopy G-Mackey functors. Instead of integer-graded (co)homology graded by dimension, we have RO(G)-graded (co)homology graded by representations. In this brief introduction, I’ll touch on the following topics: the category of G-spectra via G-universes, genuine vs. naïve G-spectra, Mackey functors and homotopy, RO(G)-grading, equivariant Eilenberg—MacLane spectra, and various kinds of fixed-points.