Integral chains and Bousfield-Kan completion
Algebraic Topology
2018-10-16 v2
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.
Keywords
Cite
@article{arxiv.1611.04157,
title = {Integral chains and Bousfield-Kan completion},
author = {Jacobson R. Blomquist and John E. Harper},
journal= {arXiv preprint arXiv:1611.04157},
year = {2018}
}
Comments
28 pages, final preprint version. arXiv admin note: text overlap with arXiv:1502.06944, arXiv:1612.08622, arXiv:1612.08623