Journal of Symplectic Geometry

Volume 17 (2019)

Number 1

The Dehn surgery characterization of the trefoil and the figure eight knot

Pages: 251 – 265

DOI: https://dx.doi.org/10.4310/JSG.2019.v17.n1.a6

Authors

Peter Ozsváth (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)

Zoltán Szabó (Department of Mathematics, Princeton University, Princeton, New Jersey, U.S.A.)

Abstract

We give a Dehn surgery characterization of the trefoil and the figure eight knots. These results are obtained by combining surgery formulas in Heegaard Floer homology from an earlier paper with the characterization of these knots in terms of their knot Floer homology due to Ghiggini.

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The first author was supported by NSF grant number DMS-050581.

The second author was supported by NSF grant number DMS-0406155.

Received 2 October 2007

Accepted 14 June 2018

Published 23 May 2019