Geometry & Topology Monographs, Vol. 7 (2004),
Proceedings of the Casson Fest,
Paper no. 7, pages 181--203.

On Heegaard Floer homology and Seifert fibered surgeries

Peter Ozsvath Zoltan Szabo

Abstract. We explore certain restrictions on knots in the three-sphere which admit non-trivial Seifert fibered surgeries. These restrictions stem from the Heegaard Floer homology for Seifert fibered spaces, and hence they have consequences for both the Alexander polynomial of such knots, and also their knot Floer homology. In particular, we show that certain polynomials are never the Alexander polynomials of knots which admit homology three-sphere Seifert fibered surgeries. The knot Floer homology restrictions, on the other hand, apply also in cases where the Alexander polynomial gives no information, such as the Kinoshita-Terasaka knots.

Keywords. Floer homology, Seifert fibered surgeries

AMS subject classification. Primary: 57R58. Secondary: 57M25.

E-print: arXiv:math.GT/0301026

Submitted to GT on 30 December 2003. (Revised 28 April 2004.) Paper accepted 21 March 2004. Paper published 18 September 2004.

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Peter Ozsvath Zoltan Szabo
Department of Mathematics, Columbia University, NY 10025, USA
Institute for Advanced Study, Princeton, NJ 08540, USA
Department of Mathematics, Princeton University, NJ 08544, USA

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