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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–equivariant homotopy theory, which we call G–model categories. We show that the diagrams in a G–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.

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Keywords
equivariant homotopy, excision
Mathematical Subject Classification 2010
Primary: 55N91, 55P91
Secondary: 55P65, 55P42
References
Publication
Received: 2 September 2014
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/