Fundamental groups as limits of discrete fundamental groups
arXiv:1710.07207 · doi:10.1112/blms.12187
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.
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