STRUCTURE THEOREMS FOR GROUPS OF HOMEOMORPHISMS OF THE CIRCLE-Reference-Cited by-同舟云学术

STRUCTURE THEOREMS FOR GROUPS OF HOMEOMORPHISMS OF THE CIRCLE

Published:2011-09 Issue:06 Volume:21 Page:1007-1036
ISSN:0218-1967
Container-title:International Journal of Algebra and Computation
language:en
Short-container-title:Int. J. Algebra Comput.

Author:

BLEAK COLLIN¹,KASSABOV MARTIN²³,MATUCCI FRANCESCO⁴

Affiliation:

1. School of Mathematics and Statistics, University of St Andrews, Mathematical Institute, North Haugh, St Andrews, Fife KY16 9SS, Scotland

2. Department of Mathematics, Cornell University, 590 Malott Hall, Ithaca, NY 14853, USA

3. School of Mathematics, University of Southampton, Southampton, SO17 1BJ, UK

4. Department of Mathematics, University of Virginia, 325 Kerchof Hall, Charlottesville, VA 22904, USA

Abstract

In this partly expository paper, we study the set [Formula: see text] of groups of orientation-preserving homeomorphisms of the circle S1 which do not admit non-abelian free subgroups. We use classical results about homeomorphisms of the circle and elementary dynamical methods to derive various new and old results about the groups in [Formula: see text]. Of the known results, we include some results from a family of results of Beklaryan and Malyutin, and we also give a new proof of a theorem of Margulis. Our primary new results include a detailed classification of the solvable subgroups of R. Thompson's group T.

Publisher

World Scientific Pub Co Pte Lt

Subject

General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0218196711006571

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1. Embedding ℚ into a finitely presented group;Bulletin of the American Mathematical Society;2022-08-11

2. Reversibility in Groups of Piecewise Linear Homeomorphisms of the Circle;Bulletin of the Malaysian Mathematical Sciences Society;2018-05-19

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4. Free products in R. Thompson’s group;Transactions of the American Mathematical Society;2013-06-19