Reparametrizations of Continuous Paths

Uli Fahrenberg, Martin Raussen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

A reparametrization (of a continuous path) is given by a surjective weakly increasing self-map of the unit interval. We show that the monoid of reparametrizations (with respect to compositions) can be understood via ``stop-maps'' that allow to investigate compositions and factorizations, and we compare it to the distributive lattice of countable subsets of the unit interval. The results obtained are used to analyse the space of traces in a topological space, i.e., the space of continuous paths up to reparametrization equivalence. This space is shown to be homeomorphic to the space of regular paths (without stops) up to increasing reparametrizations. Directed versions of the results are important in directed homotopy theory.
Original languageEnglish
JournalJournal of Homotopy and Related Structures
Volume2
Issue number2
Pages (from-to)93-117
ISSN1512-2891
Publication statusPublished - 2007

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