Australian Geometric Topology Webinar: Franco Vargas Pallete (Yale) -- Peripheral birationality for 3-dimensional convex co-compact PSL(2,C) varieties

Franco Vargas Pallete (Yale) 

Title: Peripheral birationality for 3-dimensional convex co-compact PSL(2,C) varieties 

Abstract: It is a consequence of a well-known result of Ahlfors and Bers that the PSL(2,
C) character associated to a convex co-compact hyperbolic 3-manifold is determined by
its peripheral data.  In this talk we will show how this map extends to a birational
isomorphism of the corresponding PSL(2, C) character varieties, so in particular it is
generically a 1-to-1 map.  Analogous results were proven by Dunfield in the single cusp
case, and by Klaff and Tillmann for finite volume hyperbolic 3-manifolds.  

This is joint work with Ian Agol.  

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