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Topology/Geometry Seminar

Lifting curves simply in finite covers

Priyam Patel, UC at Santa Barbara

Location:  Hill 005
Date & time: Friday, 06 October 2017 at 1:00PM - 2:00PM

Abstract:  It is a well known result of Peter Scott that the fundamental groups of surfaces are subgroup separable. This algebraic property of surface groups also has important topological implications. One such implication is that every immersed (self-intersecting) closed curve on a surface lifts to an embedded (simple) one in a finite cover of the surface. A natural question that arises is: what is the minimal degree of a cover necessary to guarantee that a given closed curve lifts to be embedded? In this talk we will discuss various results answering the above question for hyperbolic surfaces, as well as several related questions regarding the relationship between geodesic length and geometric self-intersection number.

Some of the work that will be presented is joint with T. Aougab, J. Gaster, and J. Sapir.

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