The fundamental group of reduced suspensions

We classify pointed spaces according to the first fundamental group of their reduced suspension. A pointed space is either of so-called totally path disconnected type or of horseshoe type. These two camps are defined topologically but a characterization is given in terms of fundamental groups. Among...

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Bibliographic Details
Published in:arXiv.org 2023-03
Main Authors: Corson, Samuel M, Hojka, Wolfram
Format: Article
Language:English
Subjects:
Topology
Online Access:Get full text
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Summary:We classify pointed spaces according to the first fundamental group of their reduced suspension. A pointed space is either of so-called totally path disconnected type or of horseshoe type. These two camps are defined topologically but a characterization is given in terms of fundamental groups. 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.
ISSN:2331-8422