Equivariant diagrams of spaces

Dotto, Emanuele¹

¹Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139-4307, USA

Algebraic and Geometric Topology, Tome 16 (2016) no. 2, pp. 1157-1202

Résumé

We generalize two classical homotopy theory results, the Blakers–Massey theorem and Quillen’s Theorem B, to G–equivariant cubical diagrams of spaces, for a discrete group G. We show that the equivariant Freudenthal suspension theorem for permutation representations is a direct consequence of the equivariant Blakers–Massey theorem. We also apply this theorem to generalize to G–manifolds a result about cubes of configuration spaces from embedding calculus. Our proof of the equivariant Theorem B involves a generalization of the classical Theorem B to higher-dimensional cubes, as well as a categorical model for finite homotopy limits of classifying spaces of categories.

Détail

DOI : 10.2140/agt.2016.16.1157

Keywords: equivariant, connectivity, homotopy limits

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