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A Dendrite Equivalence Relation on Loop Space

Spencer Arnesen ⟨spencer.arnesen@mathematics.byu.edu⟩

Abstract:

This talk will discuss how to turn a loop space into a group by factoring through dendrites. Inspired by the fact that group homomorphisms between fundamental groups of one-dimensional spaces induce, up to conjugation, a continuous map, and that path homotopies on one-dimensional spaces factor through a dendrite we show that homotopy through a dendrite is an equivalence relation and induces a group structure on a subset of loops. This group is always locally free.

Scheduled for: 2025-03-08 10:45 AM: Spencer Arnesen in Forbes 2070A

Status: Accepted

Collection: Continuum Theory

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