2017/01/05 by Tao Li, Li, Tao, Yoav Moriah +3
Mathematics · Medicine · #57K10 #57K30 #57M99 #Algebraic Geometry and Number Theory #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology
paper · doi:10.48550/arxiv.1701.01421
openalex publication_date 2017/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be a tunnel number one knot in M with irreducible knot exterior, where M is either S3, or a connected sum of S2× S1 with any lens space. (In particular, this includes M = S2× S1.) We prove that if a non-trivial Dehn surgery on K yields a lens space, then K is a doubly primitive knot in M. For M = S3 this resolves the tunnel number one Berge Conjecture. For M = S2× S1 this resolves a conjecture of Greene and Baker-Buck-Lecuona for tunnel number one knots.