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Proceedings of the American Mathematical Society
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
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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013962-2
PII: S 0002-9939(1990)1013962-2
Article copyright: © Copyright 1990 American Mathematical Society