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Asymmetric knots with two cyclic surgeries
by
Neil R Hoffman
University of Melbourne
Coauthors: Nathan M. Dunfield, Joan E Licata
The cyclic fillings of a hyperbolic manifold are of considerable interest. John Berge constructed a list of knots in S3 that admit a non-trivial cyclic filling and the Berge conjecture states that this list is complete. A consequence of the Berge Conjecture is that all such knot complements admit an order two symmetry. While the natural generalization of the Berge Conjecture still provides a list of hyperbolic manifolds with two cyclic fillings, we show such a list is incomplete. Finally, this provides examples of L-spaces which are not the double branched covers of knots in S3.
Date received: October 20, 2015
Copyright © 2015 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cblw-14.