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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Centralizers of immersions of the circle


Author: Carlos Arteaga
Journal: Proc. Amer. Math. Soc. 109 (1990), 849-853
MSC: Primary 58F10; Secondary 20F38, 58D10
DOI: https://doi.org/10.1090/S0002-9939-1990-1013962-2
MathSciNet review: 1013962
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Abstract: We prove here that for every element $f$ of an open and dense subset of immersions of the circle ${S^1}$, either the centralizer $Z\left ( f \right )$ of $f$ is trivial (i.e. $f$ only commutes with its own powers) or $f$ is topologically conjugate to a map ${f_n}:{S^1} \to {S^1}$ given by ${f_n}\left ( z \right ) = {z^n}$ and, in this case, if $h$ is the conjugacy between $f$ and ${f_n}$ then $Z\left ( f \right )$ is a subgroup of $\left \{ {{h^{ - 1}} \circ \omega {f_m} \circ h;m \in {\mathbf {N}}{\text { and }}{\omega ^{n - 1}} = 1} \right \}$.


References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1990 American Mathematical Society