Lens space surgeries & primitive/Seifert type constructions

2007/12/11 by Michael J. Williams, Williams, Michael J.
Mathematics · #57M25 #FOS: Mathematics #Geometric Topology (math.GT) #math.GT #msc:57M25

paper · pdf · doi:10.48550/arxiv.0712.1797

18 pages, 8 figures

arxiv created 2007/12/11 · arxiv updated 2009/12/01

Abstract

We show that lens space surgeries on knots in S³ 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.

Related

• Tunnel number one knots satisfy the Berge Conjecture
• Some knots in S¹ x S² with lens space surgeries
• Reducible surgery in lens spaces and seiferters
• Lens space surgeries and L-space homology spheres
• The lens space realization problem