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

2006/04/04 by Peter Ozsváth, Zoltán Szabó, Ozsvath, Peter +1 · 4 citations
Mathematics · Medicine · #53D #57R #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.math/0604079

openalex publication_date 2006/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give a Dehn surgery characterization of the trefoil and the figure eight knots. These results are gotten 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 given in a recent paper of Ghiggini.

Citations

• Holomorphic disks and knot invariants

Cited by

• Links have no characterising slopes
• Non-characterizing slopes for more 3-manifolds
• Unique Surgery Descriptions along Knots
• Dehn surgery functions are never injective

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• Heegaard Floer Surgery Formula and Cosmetic Surgeries
• A general Heegaard Floer surgery formula
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• Cosmetic surgeries on knots in S³
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