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.

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Keywords
equivariant homotopy, excision
Mathematical Subject Classification 2010
Primary: 55N91, 55P91
Secondary: 55P65, 55P42