On equivariant homotopy theory for model categories

By Marc Stephan. 2013

53 citations recorded by the source corpus.

We introduce and compare two approaches to equivariant homotopy theory in a topological or ordinary Quillen model category. For the topological model category of spaces, we generalize Piacenza's result that the categories of topological presheaves indexed by the orbit category of a fixed topological group $G$ and the category of $G$-spaces can be endowed with Quillen equivalent model category structures. We prove an analogous result for any cofibrantly generated model category and discrete group $G$, under certain conditions on the fixed point functors of the subgroups of $G$. These conditions hold in many examples, though not in the category of chain complexes, where we nevertheless establish and generalize to collections an equivariant Whitehead Theorem \`{a} la Kropholler and Wall for the normalized chain complexes of simplicial $G$-sets.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f3a841db61d33d4f0c163e7ff2ce47725419873b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Theory and Mathematics

1. L. Pereira
2. P. Bonventre

In Geometry and Topology

1. L. Pereira
2. P. Bonventre

In Mathematical Physics

1. L. Pereira
2. P. Bonventre

Citations in the corpus

• Genuine equivariant operads (2017, background): “The exact condition, originally from [11] and updated in [28], can be found in Definition 6.”