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Singular chains and the fundamental group

Volume 253 / 2021

Manuel Rivera, Mahmoud Zeinalian Fundamenta Mathematicae 253 (2021), 297-316 MSC: Primary 55P15, 55U40; Secondary 57T30, 55P35. DOI: 10.4064/fm734-6-2020 Published online: 17 November 2020

Abstract

We show that the natural algebraic structure of the singular chains on a path-connected topological space determines the isomorphism class of the fundamental group functorially. Moreover, we describe a notion of weak equivalence for the relevant algebraic structure under which the isomorphism class of the fundamental group is preserved.

Authors

  • Manuel RiveraDepartment of Mathematics
    Purdue University
    150 N. University Street
    West Lafayette, IN 47907-2067, U.S.A.
    e-mail
  • Mahmoud ZeinalianDepartment of Mathematics
    City University of New York
    Lehman College
    250 Bedford Park Blvd W
    Bronx, NY 10468, U.S.A.
    e-mail

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