Integral chains and Bousfield-Kan completion

2016/11/13 by Blomquist, Jacobson R., Harper, John E.
#55N10 #55P60 #55P99 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.1611.04157

Abstract

Working in the Arone-Ching framework for homotopical descent, it follows that the Bousfield-Kan completion map with respect to integral homology is the unit of a derived adjunction. We prove that this derived adjunction, comparing spaces with coalgebra complexes over the associated integral homology comonad, via integral chains, can be turned into a derived equivalence by replacing spaces with the full subcategory of simply connected spaces. In particular, this provides an integral chains characterization of the homotopy type of simply connected spaces.

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