A complete characterization of reversibility in PL(S)

An element g in a group G is called reversible if g−1=hgh−1 for some h∈G. We give a complete characterization of reversibility in the group PL(S) of piecewise linear homeomorphisms of the circle with finite number of break points. This work is the continuation of the study done by K. Ben Rejeb and H...

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Bibliographic Details
Published inJournal of mathematical analysis and applications Vol. 528; no. 1; p. 127553
Main Author Ben Rejeb, Khadija
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.12.2023
Subjects
Involution
Jump
Piecewise linear homeomorphism of the circle with finite break points
Reversible
Rotation number
Strongly reversible
Piecewise linear homeomorphism of the circle with finite break points
Reversible
Involution
Rotation number
Jump
Strongly reversible
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Summary:An element g in a group G is called reversible if g−1=hgh−1 for some h∈G. We give a complete characterization of reversibility in the group PL(S) of piecewise linear homeomorphisms of the circle with finite number of break points. This work is the continuation of the study done by K. Ben Rejeb and H. Marzougui in (2019) [2], in particular we answer a question raised in it. This work is also a comparison and an extension to results of reversibility in the groups PL(R) and Homeo(S); some interesting examples are constructed here to answer questions that can be raised in this subject.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2023.127553