Azumaya algebras and hyperbolic knots

Expositor: Matthew Stover
05/10/2017 , 15:30 | Sala 236

I will talk about arithmetic geometry of SL(2,C) character varieties of hyperbolic knots. A simple criterion on roots of the Alexander polynomial determines whether or not a natural construction extends to determine a so-called Azumaya algebra over the entire canonical component of the character variety, and I'll then explain how this forces significant restrictions on arithmetic invariants of Dehn surgeries on the knot. This is joint work with Ted Chinburg and Alan Reid.