Cosmetic surgeries on genus one knots

Wang, Jiajun

doi:10.2140/agt.2006.6.1491

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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

Volume 6, issue 3 (2006)