Homotopy theory of G–diagrams and equivariant excision

Dotto, Emanuele; Moi, Kristian

doi:10.2140/agt.2016.16.325

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Homotopy theory of $G$–diagrams and equivariant excision

Emanuele Dotto and Kristian Moi

Algebraic & Geometric Topology 16 (2016) 325–395

DOI: 10.2140/agt.2016.16.325

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.

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/

Volume 16, issue 1 (2016)