Browsing by Author "Reid, Alan"
Now showing 1 - 2 of 2
Results Per Page
Sort Options
Item Embargo On a conjecture of Chinburg-Reid-Stover(2022-04-21) Rouse, Nicholas; Reid, AlanWe study a conjecture of Chinburg-Reid-Stover about ramification sets of quaternion algebras associated to hyperbolic 3-orbifolds obtained by (d,0) Dehn surgery on hyperbolic knot complements in S^3. For a sporadic example and an infinite family, we prove that the set of rational primes p such that there is some d such that the quaternion algebra associated to the (d,0) surgery is ramified at some prime ideal above p is infinite. This behavior is governed by the Alexander polynomial of the knot, and we investigate its connection to reducible representations on the canonical component of the character variety and the failure of a certain function field quaternion algebra to extend to an Azumaya algebra over the canonical component. We further provide a more general framework for finding such examples that one may use to recover the infinite family.Item Some remarks on group actions on hyperbolic 3-manifolds(University of Primorska, 2022) Reid, Alan; Salgueiro, AntonioWe prove that there are infinitely many non-commensurable closed orientable hyperbolic 3-manifolds X, with the property that there are finite groups G1 and G2 acting freely by orientation-preserving isometries on X with X/G1 and X/G2 isometric, but G1 and G2 are not conjugate in Isom(X). We provide examples where G1 and G2 are non-isomorphic, and prove analogous results when G1 and G2 act with fixed-points.