A complete list of lens spaces constructed by Dehn surgery I

2010/05/19 by Motoo Tange, Tange, Motoo
Mathematics · #57M25 #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1005.3512

openalex publication_date 2010/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Berge in [1] defined doubly primitive knots, which yield lens spaces by Dehn surgery. At the same paper he listed the knots into several types. In this paper we will prove the list is complete when τ>1. The invariant τ is a quantity with regard to lens space surgery, which is defined in this paper. Furthermore at the same time we will also prove that Table~6 in [8] is complete as Poincaré homology sphere surgery when τ>1.

Related

• The lens space realization problem
• Homology spheres yielding lens spaces
• Jointly primitive knots and surgeries between lens spaces
• Three lens space summands from the Poincaré homology sphere
• Dehn surgery on complicated fibered knots in the 3-sphere