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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Quasisymmetric groups
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by Vladimir Markovic PDF
J. Amer. Math. Soc. 19 (2006), 673-715 Request permission

Abstract:

One of the first problems in the theory of quasisymmetric and convergence groups was to investigate whether every quasisymmetric group that acts on the sphere $\textbf {S}^{n}$, $n>0$, is a quasisymmetric conjugate of a Möbius group that acts on $\textbf {S}^{n}$. This was shown to be true for $n=2$ by Sullivan and Tukia, and it was shown to be wrong for $n>2$ by Tukia. It also follows from the work of Martin and of Freedman and Skora. In this paper we settle the case of $n=1$ by showing that any $K$-quasisymmetric group is $K_1$-quasisymmetrically conjugated to a Möbius group. The constant $K_1$ is a function $K$.
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Additional Information
  • Vladimir Markovic
  • Affiliation: University of Warwick, Institute of Mathematics, Coventry CV4 7AL, United Kingdom
  • Email: markovic@maths.warwick.ac.uk
  • Received by editor(s): December 15, 2004
  • Published electronically: January 25, 2006
  • © Copyright 2006 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: J. Amer. Math. Soc. 19 (2006), 673-715
  • MSC (2000): Primary 20H10, 37F30
  • DOI: https://doi.org/10.1090/S0894-0347-06-00518-2
  • MathSciNet review: 2220103