3 papers
math.RA2025
Extending degree-2 Azumaya algebras with C2-actions and examples from character varieties of knot group
Justin Lawrence, Nicholas Rouse, Ben Williams
We give criteria to determine when a degree-2 Azumaya algebra with -action over a dense open subvariety of a curve extends to the entire curve as an algebra with -action.…
math.GT2021
A conjecture of Chinburg-Reid-Stover for surgeries on twist knots
Nicholas Rouse
Associated to a hyperbolic knot complement in is a set of prime numbers corresponding to the residue characteristics of the ramified places of the quaternion algebras obtaine…
math.GT2020
Infinitely many knots with non-integral trace
Alan W. Reid, Nicholas Rouse
We prove that there are infinitely many non-homeomorphic hyperbolic knot complements for which contains elements whose trace is an algeb…