Surgery descriptions and volumes of Berge knots I: Large volume Berge knots

2005/09/02 by Kenneth L. Baker, Baker, Kenneth L.
Mathematics · Medicine · #57M50 (Primary) 57M25 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Surgical Sutures and Adhesives #math.GT #msc:57M25 #msc:57M50

paper · pdf · doi:10.48550/arxiv.math/0509054

18 pages, 19 figures

arxiv created 2005/09/02 · openalex publication_date 2005/09/02 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By obtaining surgery descriptions of knots which lie on the genus one fiber of the trefoil or figure eight knot, we show that these include hyperbolic knots with arbitrarily large volume. These knots admit lens space surgeries and form two families of Berge knots. By way of tangle descriptions we also obtain surgery descriptions for these knots on minimally twisted chain links.

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