Isometry groups of infinite-genus hyperbolic surfaces

Abstract:

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 \(G\) is finite, Allcock’s construction yields a closed surface. Otherwise, the construction gives an infinite-genus surface.

In this talk, we discuss a related question. We fix any infinite-genus surface \(S\) and characterise 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.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( slides | video )

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Geometry and topology online

Series comments: You can also find up-to-date information on the seminar homepage - warwick.ac.uk/fac/sci/maths/research/events/seminars/areas/geomtop/

The talks start five minutes after the hour. Talks are typically 55 minutes long, including time for questions.

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