The fundamental group of reduced suspensions
Volume 264 / 2024
Fundamenta Mathematicae 264 (2024), 217-239
MSC: Primary 14F35; Secondary 55P40, 57M30
DOI: 10.4064/fm309-11-2023
Published online: 8 February 2024
Abstract
We classify pointed spaces according to the fundamental group of their reduced suspension. A pointed space is either of horseshoe type or has fundamental group isomorphic to that of a totally path disconnected space. Among totally path disconnected spaces, the fundamental group is shown to be a complete invariant for a notion of topological equivalence weaker than that of homeomorphism.
