2009/11/12 by Kitroser, Daniel
#FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.0911.2408
A group action is said to be highly-transitive if it is k-transitive for every k ≥ 1. 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 Sym(Z) 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.