Lens space surgeries & primitive/Seifert type constructions
Michael J. Williams

TL;DR
This paper demonstrates that certain lens space surgeries on knots in the 3-sphere, originating from primitive/Seifert constructions, also originate from primitive/primitive constructions, advancing the understanding of the Berge conjecture.
Contribution
It establishes a link between primitive/Seifert and primitive/primitive constructions for lens space surgeries, aiding the proof of the Berge conjecture for tunnel number one knots.
Findings
Lens space surgeries from primitive/Seifert also come from primitive/primitive constructions.
Progress towards proving the Berge conjecture for tunnel number one knots.
First step in a three-step program for the Berge conjecture.
Abstract
We show that lens space surgeries on knots in which arise from the primitive/Seifert type construction also arise from the primitive/primitive construction. This is the first step of a three step program to prove the Berge conjecture for tunnel number one knots.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models
