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Equivariant diagrams of spaces
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.Comment: 36 pages. arXiv admin note: text overlap with arXiv:1410.764
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