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Möbius-like groups of homeomorphisms of the circle

Citation

Kovačević, Nataša (1994) Möbius-like groups of homeomorphisms of the circle. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/vy4w-j074. https://resolver.caltech.edu/CaltechTHESIS:05082013-102143473

Abstract

A group G → Homeo_+(S^1) is a Möbius-like group if every element of G is conjugate in Homeo(S^1) to a Mobius transformation. Our main result is: given a Mobus like like group G which has at least one global fixed point, G is conjugate in Homeo(S^1) to a Möbius group if and only if the limit set of G is all of S^1 . Moreover, we prove that if the limit set of G is not SI, then after identifying some closed subintervals of S^1 to points, the induced action of G is conjugate to an action of a Möbius group.

We also show that the above result does not hold in the case when G has no global fixed points. Namely, we construct examples of Möbius-like groups with limit set equal to S^1, but these groups cannot be conjugated to Möbius groups.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Mathematics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gabai, David
Thesis Committee:
  • Unknown, Unknown
Defense Date:23 May 1994
Record Number:CaltechTHESIS:05082013-102143473
Persistent URL:https://resolver.caltech.edu/CaltechTHESIS:05082013-102143473
DOI:10.7907/vy4w-j074
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:7674
Collection:CaltechTHESIS
Deposited By: Benjamin Perez
Deposited On:08 May 2013 18:13
Last Modified:19 Apr 2021 22:28

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