Rigidity and exotic models for $$v_1$$-local G-equivariant stable homotopy theory

Equivariant stable homotopy theory

We will study equivariant homotopy theory for G a finite group (although this often easily generalizes to compact Lie groups). The general idea is that if we have two G-spaces X and Y , we’d like to study homotopy classes of equivariant maps between them: [X,Y ] = Map(X,Y )/htpy, where Map(X,Y ) = {f : X → Y |f(gx) = gf(x) for all g ∈ G}. In classical homotopy theory (i.e. when G is the trivial...

Rigidity and exotic models for the K –local stable homotopy category

A Survey of Equivariant Stable Homotopy Theory

EQUIVARIANT stable homotopy theory was invented by G. B. Segal in the early 1970s [45]. He was motivated by his work with Atiyah [9] on equivariant K-theory, generalizing an earlier theorem of Atiyah’s on the K-theory of classifying spaces of finite groups to compact Lie groups, and by his work on configuration space and discrete models for iterated loop spaces. His work also suggested to him t...

Spectral Sequences in (equivariant) Stable Homotopy Theory

1. The homotopy fixed-point spectral sequence: 5/15/17 Today, Richard spoke about the homotopy fixed-point spectral sequence in equivariant stable homotopy theory. We’ll start with the Bousfield-Kan spectral sequence (BKSS). One good reference for this is Guillou’s notes [4], and Hans Baues [2] set it up in a general model category. We’ll work in sSet, so that everything is connective. Consider...

An Algebraic Model for Rational S-equivariant Stable Homotopy Theory

Greenlees defined an abelian category A whose derived category is equivalent to the rational S1-equivariant stable homotopy category whose objects represent rational S1equivariant cohomology theories. We show that in fact the model category of differential graded objects in A models the whole rational S1-equivariant stable homotopy theory. That is, we show that there is a Quillen equivalence be...