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Isometry groups of infinite-genus hyperbolic surfaces


Speaker: Priyam Patel, University of Utah
Location: Zoom
Start time: Tue, Jun 2 2020, 1:40PM

Allcock, building on the work of Greenburg, proved that for any countable group G, there is a a complete hyperbolic surface whose isometry group is exactly G. When the group is finite, Allcock’s construction yields a closed surface, but when it is not finite, the construction gives an infinite-genus surface.

In this talk, we discuss a related question. We fix any infinite-genus surface S and characterize all groups that can arise as the isometry group for a complete hyperbolic structure on S. In the process, we give a classification type theorem for infinite-genus surfaces and, if time allows, two applications of the main result. This talk is based on joint work with T. Aougab and N. Vlamis.

Zoom meeting ID: 120-952-219. UPDATE: there will not be teatime with the speaker before the talk.