Volume 7 (2004)

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On Heegaard Floer homology and Seifert fibered surgeries

Peter Ozsvath and Zoltan Szabo

Geometry & Topology Monographs 7 (2004) 181–203

DOI: 10.2140/gtm.2004.7.181

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

Mathematical Subject Classification

Primary: 57R58

Secondary: 57M25

References
Publication

Received: 30 December 2003
Revised: 28 April 2004
Accepted: 21 March 2004
Published: 18 September 2004

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