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math.GT2023
Types of Symmetries of Knots
Keegan Boyle, Nicholas Rouse, Ben Williams
We classify all finite group actions on knots in the 3-sphere. By geometrization, all such actions are conjugate to actions by isometries, and so we may use orthogonal representati…
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…