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Homological epimorphisms, homotopy epimorphisms and acyclic maps

Chuang, J. & Lazarev, A. (2020). Homological epimorphisms, homotopy epimorphisms and acyclic maps. Forum Mathematicum, doi: 10.1515/forum-2019-0249


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.

Publication Type: Article
Publisher Keywords: Homotopy epimorphism; homological epimorphism; plus-construction; acyclic map; 16E45; 55R35
Subjects: Q Science > QA Mathematics
Departments: School of Science & Technology > Mathematics
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