Highly-transitive actions of surface groups
Author:
Daniel Kitroser
Journal:
Proc. Amer. Math. Soc. 140 (2012), 3365-3375
MSC (2010):
Primary 20B22, 20B35
DOI:
https://doi.org/10.1090/S0002-9939-2012-11195-5
Published electronically:
April 24, 2012
MathSciNet review:
2929006
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Abstract | References | Similar Articles | Additional Information
Abstract: A group action is said to be highly-transitive if it is -transitive for every
. The main result of this thesis is the following:
Main Theorem. The fundamental group of a closed, orientable surface of genus admits a faithful, highly-transitive action on a countably infinite set.
From a topological point of view, finding a faithful, highly-transitive action of a surface group is equivalent to finding an embedding of the surface group into with a dense image. In this topological setting, we use methods that were originally developed for densely embedding surface groups in locally compact groups.
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Additional Information
Daniel Kitroser
Affiliation:
Department of Mathematics, Ben-Gurion University of The Negev, Be’er Sheva, Israel
Email:
kitrosar@bgu.ac.il
DOI:
https://doi.org/10.1090/S0002-9939-2012-11195-5
Received by editor(s):
December 15, 2010
Received by editor(s) in revised form:
April 11, 2011
Published electronically:
April 24, 2012
Additional Notes:
The author was partially supported by ISF grant 888/07
Communicated by:
Daniel Ruberman
Article copyright:
© Copyright 2012
American Mathematical Society