Homological epimorphisms and homotopy epimorphisms
Algebraic Topology
2021-06-15 v2
Abstract
We show that the notions of homotopy epimorphism and homological epimorphism in the category of differential graded algebras are equivalent. As an application we obtain a characterization of acyclic maps of topological spaces in terms of induced maps of their chain algebras of based loop spaces. In the case of a universal acyclic map we obtain, for a wide class of spaces, an explicit algebraic description for these induced maps in terms of derived localization.
Cite
@article{arxiv.1908.11283,
title = {Homological epimorphisms and homotopy epimorphisms},
author = {Joe Chuang and Andrey Lazarev},
journal= {arXiv preprint arXiv:1908.11283},
year = {2021}
}
Comments
12 pages. In this version an erroneous definition of an acyclic map has been corrected; this has not affected the rest of the paper