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Interactions Between Hyperbolic Geometry, Quantum Topology and Number Theory
June 3-19, 2009
Columbia University
New York, USA

Organizers
Abhijit Champanerkar (CSI, CUNY), Oliver Dasbach (LSU), Effie Kalfagianni (MSU), Ilya Kofman (CSI, CUNY), Walter Neumann (Barnard College, Columbia U.), Neal Stoltzfus (LSU)

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Commensurability of knot complements
by
Genevieve Walsh
Tufts University
Coauthors: Michel Boileau, Steve Boyer

Two three-manifolds are commensurable if they admit homeomorphic finite-sheeted covers. Here we investigate the commensurability classes of hyperbolic 3-manifolds. We show that if K is a hyperbolic knot without hidden symmetries, then there are at most three knot complements in the commensurability class of S3 \K. We will discuss various ways in which knots can be commensurable, and in particular we give a characterization of cyclically commensurable knots which are periodic. This is joint work with Michel Boileau and Steve Boyer.

Date received: May 28, 2009

Copyright © 2009 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cayy-21.