Singular chains and the fundamental group
Volume 253 / 2021
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.
