Department of Mathematics

Colloquium

  •  Arithmetic of Dehn surgery points and Azumaya algebras
  •  10/26/2017
  •  4:10 PM - 5:00 PM
  •  C304 Wells Hall
  •  Alan Reid, Rice University

Associated to a finite volume hyperbolic 3-manifold is a number field and a 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 a certain curve component (the so-called canonical component) of the SL(2,C)-character variety of the knot group. This talk will give examples of different behavior and survey recent work on how the varying behavior can be explained using the language of Azumaya algebras over the canonical curve.

 

Contact

Department of Mathematics
Michigan State University
619 Red Cedar Road
C212 Wells Hall
East Lansing, MI 48824

Phone: (517) 353-0844
Fax: (517) 432-1562

College of Natural Science