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Homological epimorphisms, homotopy epimorphisms and acyclic maps

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Homological epimorphisms, homotopy epimorphisms and acyclic maps. / Chuang, Joseph; Lazarev, Andrey.
In: Forum Mathematicum, Vol. 32, No. 6, 01.11.2020, p. 1395–1406.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Chuang, J & Lazarev, A 2020, 'Homological epimorphisms, homotopy epimorphisms and acyclic maps', Forum Mathematicum, vol. 32, no. 6, pp. 1395–1406. https://doi.org/10.1515/forum-2019-0249

APA

Chuang, J., & Lazarev, A. (2020). Homological epimorphisms, homotopy epimorphisms and acyclic maps. Forum Mathematicum, 32(6), 1395–1406. https://doi.org/10.1515/forum-2019-0249

Vancouver

Chuang J, Lazarev A. Homological epimorphisms, homotopy epimorphisms and acyclic maps. Forum Mathematicum. 2020 Nov 1;32(6):1395–1406. Epub 2020 Jul 16. doi: 10.1515/forum-2019-0249

Author

Chuang, Joseph ; Lazarev, Andrey. / Homological epimorphisms, homotopy epimorphisms and acyclic maps. In: Forum Mathematicum. 2020 ; Vol. 32, No. 6. pp. 1395–1406.

Bibtex

@article{3d635d79fedd46e29848e1c66d8dea0e,
title = "Homological epimorphisms, homotopy epimorphisms and acyclic maps",
abstract = "We show that the notions of homotopy epimorphism and homological epimorphismin 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.",
author = "Joseph Chuang and Andrey Lazarev",
year = "2020",
month = nov,
day = "1",
doi = "10.1515/forum-2019-0249",
language = "English",
volume = "32",
pages = "1395–1406",
journal = "Forum Mathematicum",
issn = "0933-7741",
publisher = "Walter de Gruyter GmbH",
number = "6",

}

RIS

TY - JOUR

T1 - Homological epimorphisms, homotopy epimorphisms and acyclic maps

AU - Chuang, Joseph

AU - Lazarev, Andrey

PY - 2020/11/1

Y1 - 2020/11/1

N2 - We show that the notions of homotopy epimorphism and homological epimorphismin 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.

AB - We show that the notions of homotopy epimorphism and homological epimorphismin 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.

U2 - 10.1515/forum-2019-0249

DO - 10.1515/forum-2019-0249

M3 - Journal article

VL - 32

SP - 1395

EP - 1406

JO - Forum Mathematicum

JF - Forum Mathematicum

SN - 0933-7741

IS - 6

ER -