Lens space surgeries and a conjecture of Goda and Teragaito

Rasmussen, Jacob

doi:10.2140/gt.2004.8.1013

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Lens space surgeries and a conjecture of Goda and Teragaito

Jacob Rasmussen

Geometry & Topology 8 (2004) 1013–1031

DOI: 10.2140/gt.2004.8.1013

arXiv: math.GT/0405114

Abstract

Using work of Ozsváth and Szabó, we show that if a nontrivial knot in $S^{3}$ admits a lens space surgery with slope $p$ , then $p \leq 4 g + 3$ , where $g$ is the genus of the knot. This is a close approximation to a bound conjectured by Goda and Teragaito.

Keywords

lens space surgery, Seifert genus, Heegaard Floer homology

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57R58

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Publication

Received: 13 May 2004

Accepted: 11 July 2004

Published: 7 August 2004

Proposed: Peter Ozsvath

Seconded: Tomasz Mrowka, Peter Kronheimer

Authors

Jacob Rasmussen
Department of Mathematics Princeton University Princeton New Jersey 08544 USA

Volume 8, issue 3 (2004)