|4:00 pm Monday, August 28, 2017|
Topology Seminar: Arithmetic of Dehn surgery points and Azumaya algebras over canonical curves.
by Alan Reid (Rice) in HBH 427
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. The talk will investigate this, and give examples of different behavior. The main results will show how the varying behavior can be explained using the language of Azumaya algebras over a curve. This is joint work with Ted Chinburg and Matthew Stover.Host Department: Rice University-Mathematics
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