#### Volume 16, issue 1 (2016)

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Homotopy theory of $G$–diagrams and equivariant excision

### Emanuele Dotto and Kristian Moi

Algebraic & Geometric Topology 16 (2016) 325–395
##### Abstract

Let $G$ be a finite group. We define a suitable model-categorical framework for $G\phantom{\rule{0.3em}{0ex}}$–equivariant homotopy theory, which we call $G\phantom{\rule{0.3em}{0ex}}$–model categories. We show that the diagrams in a $G\phantom{\rule{0.3em}{0ex}}$–model category which are equipped with a certain equivariant structure admit a model structure. This model category of equivariant diagrams supports a well-behaved theory of equivariant homotopy limits and colimits. We then apply this theory to study equivariant excision of homotopy functors.

##### Keywords
equivariant homotopy, excision
##### Mathematical Subject Classification 2010
Primary: 55N91, 55P91
Secondary: 55P65, 55P42
##### Publication
Revised: 11 April 2015
Accepted: 7 May 2015
Published: 23 February 2016
##### Authors
 Emanuele Dotto Department of Mathematics Massachusetts Institute of Technology 77 Massachusetts Avenue Cambridge, MA 02139-4307 USA http://math.mit.edu/~dotto/ Kristian Moi Department of Mathematical Sciences University of Copenhagen Universitetsparken 5 DK-2100 Copenhagen Denmark http://www.math.uni-muenster.de/u/moi/