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

Primary: 57M27, 57R58

Secondary: 53D40

References

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Publication

Received: 26 February 2006
Revised: 26 July 2006
Accepted: 17 August 2006
Published: 4 October 2006

Authors