Homotopy theory of G–diagrams and equivariant excision

Equivariant Homotopy Theory

In this note we announce an obstruction theory for extending (continuous) equivariant maps defined on a certain class of G-spaces, where G is a compact Lie group. The details of this work will be published elsewhere. Our results barely touch upon the attendant problem of providing techniques that would serve in practice for the computation of the obstruction groups. In general this last problem...

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...

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...

Characters in Global Equivariant Homotopy Theory

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...