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Arithmetic of Dehn surgery points

Presented by: 
Alan Reid University of Texas at Austin
Date: 
Tuesday 9th May 2017 - 14:30 to 15:30
Venue: 
INI Seminar Room 1
Abstract: 
Associated to a finite volume hyperbolic 3-manifold is a number field and quaternion algebra over that number field.
Closed hyperbolic 3-manifolds arising from Dehn surgeries on a hyperbolic knot complement provide a family of number fields and
quaternion algebras that can be viewed as varying over the canonical component of the character variety of the knot.  This talk will investigate this, and  give examples of different behavior. The main results will show how this can be explained using the language of Azumaya algebras over a curve. This is joint work with Ted Chinburg and Matthew Stover.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons