English

Fundamental groups as limits of discrete fundamental groups

General Topology 2018-08-01 v2 Geometric Topology Metric Geometry

Abstract

In this note we investigate to what extent the fundamental group of a metric space can be described as the inverse limit of its discrete fundamental groups. We show that some mild conditions suffice to imply the existence of an isomorphism and we provide a list of counterexamples to possible weakenings of these hypotheses.

Keywords

Cite

@article{arxiv.1710.07207,
  title  = {Fundamental groups as limits of discrete fundamental groups},
  author = {Federico Vigolo},
  journal= {arXiv preprint arXiv:1710.07207},
  year   = {2018}
}

Comments

11 pages, 9 figures. Example 5.3 had to be deeply modified and was completely rewritten. To be published in the Bulletin of the LMS