Covers and curves

Abstract:

It is a celebrated result of Scott that every closed curve on a hyperbolic surface \(S\) lifts to a simple closed curve on some finite cover. In the spirit of this work we pose the following question: "What information about two covers \(X\) and \(Y\) of \(S\) can be derived by understanding how curves on \(S\) lift simply to \(X\) and \(Y\)?" In this talk, we will explore the answer to this question for regular finite covers of a closed hyperbolic surface.

This is joint work with Tarik Aougab, Max Lahn, and Yang (Sunny) Xiao.

algebraic topologydifferential geometrydynamical systemsgroup theorygeometric topologysymplectic geometry

Audience: researchers in the topic

( chat | paper | slides )

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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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