Singular chains and the fundamental group
Algebraic Topology
2020-06-17 v4
Abstract
We show that the natural algebraic structure of the singular chains on a path connected topological space determines the fundamental group functorially. Moreover, we describe a notion of weak equivalence for the relevant algebraic structure under which the data of the fundamental group is preserved.
Cite
@article{arxiv.1807.06410,
title = {Singular chains and the fundamental group},
author = {Manuel Rivera and Mahmoud Zeinalian},
journal= {arXiv preprint arXiv:1807.06410},
year = {2020}
}
Comments
The presentation was revised and reorganized. Minor typos were corrected, new references were added. To appear on Fundamenta Mathematicae