New York Journal of Mathematics
Volume 24 (2018), 870-896


Keegan Boyle

On the virtual cosmetic surgery conjecture

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Published: October 6, 2018.
Keywords: knots, covering spaces, orbifolds, hyperbolic geometry.
Subject: 57M10, 57M25.

Let K be a knot in S3, and M and M' be distinct Dehn surgeries along K. We investigate when M covers M'. When K is a torus knot, we provide a complete classification of such covers. When K is a hyperbolic knot, we provide partial results in the direction of the conjecture that M never covers M'.


I would like to thank the referee on a previous version for useful comments, Nathan Dunfield, Jessica Purcell, and Cameron Gordon for helpful conversations, and Robert Lipshitz for support, suggestions, and corrections.

Author information

Keegan Boyle:
Department of Mathematics
University of Oregon
Eugene, OR 97403, USA.