Abstract

Equivariant stable homotopy theory considers spaces and spectra endowed with the action of a fixed group G. Classically, this group has been taken to be finite or compact Lie, but here we will consider only the case of a finite group acting. Our goal is to produce a broad-strokes overview of the state of equivariant stable homotopy theory, focusing the intuition behind many of the objects and constructions, exploring some of the tools in equivariant algebra, and showing how one can compute with these as easily as one computes classically.