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Cosmetic surgeries on genus one knots

Jiajun Wang
Algebraic & Geometric Topology 6 (2006) 1491–1517
DOI: 10.2140/agt.2006.6.1491

arXiv: math.GT/0512253
Abstract

In this paper, we prove that there are no truly cosmetic surgeries on genus one classical knots. If the two surgery slopes have the same sign, we give the only possibilities of reflectively cosmetic surgeries. The result is an application of Heegaard Floer theory and number theory.

Keywords
cosmetic surgery, knot, Heegaard Floer homology, cyclotomic number
Mathematical Subject Classification 2000
Primary: 57M27, 57R58
Secondary: 53D40
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Publication
Received: 26 February 2006
Revised: 26 July 2006
Accepted: 17 August 2006
Published: 4 October 2006
Authors
Jiajun Wang
Department of Mathematics
University of California at Berkeley
Berkeley, CA 94720
USA