Singular chains and the fundamental group

Manuel Rivera, Mahmoud Zeinalian

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish (US)
Pages (from-to)297-316
Number of pages20
JournalFundamenta Mathematicae
Volume253
Issue number3
DOIs
StatePublished - 2021

Keywords

  • Bar-cobar duality
  • dg coalgebra
  • Fundamental group
  • Singular chains

ASJC Scopus subject areas

  • Algebra and Number Theory

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