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Abstract
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We generalize two classical homotopy theory results, the
Blakers–Massey theorem and Quillen’s Theorem B, to
–equivariant
cubical diagrams of spaces, for a discrete group
.
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
–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.
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Keywords
equivariant, connectivity, homotopy limits
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Mathematical Subject Classification 2000
Primary: 55P91
Secondary: 55Q91
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Publication
Received: 19 June 2015
Accepted: 23 July 2015
Published: 26 April 2016
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