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Quasisymmetric groups

Markovic, Vladimir (2006) Quasisymmetric groups. Journal of the American Mathematical Society, 19 (03). pp. 673-716. ISSN 0894-0347.

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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 S^n, n > 0, is a quasisymmetric conjugate of a Möbius group that acts on 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:© 2006 American Mathematical Society. Received by the editors December 15, 2004.
Issue or Number:03
Classification Code:2000 Mathematics Subject Classification. Primary 20H10, 37F30
Record Number:CaltechAUTHORS:20170505-150848927
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77240
Deposited By: Ruth Sustaita
Deposited On:05 May 2017 22:32
Last Modified:03 Oct 2019 17:55

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