Year: 2025
Type: article
Abstract: Let K be a tunnel number one knot in M with irreducible knot exterior, where M is either S 3 , or a connected sum of S 2 S 1 with any lens space.(In particular, this includes M D S 2 S 1 .)We prove that if a nontrivial Dehn surgery on K yields a lens space, then K is a doubly primitive knot in M. For M D S 3 this resolves the tunnel number one Berge conjecture.For M D S 2 S 1 this resolves a conjecture of Greene and Baker, Buck and Lecuona for tunnel number one knots.
Source: Geometry & Topology
Authors: Tao Li, Yoav Moriah, Tali Pinsky
Institutions: Boston College, Technion – Israel Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Funder: National Science Foundation
OpenAlex ID: W2995522495