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Highly Transitive Actions of Surface Groups
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
> 1 admits a faithfull, highly-transitive action on a countably infinite set.
From a topological point of view, finding a faithfull, 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 originally developed in [3] and [1] for densely embedding surface
groups in locally compact groups
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