Cabling Conjecture for Small Bridge Number

2015/07/06 by Grove, Colin
Biochemistry, Genetics and Molecular Biology · Mathematics · #57M25 #Connective tissue disorders research #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1507.01317

openalex publication_date 2015/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let k⊂ S³ be a nontrivial knot. The Cabling Conjecture of Francisco González-Acuña and Hamish Short posits that π-Dehn surgery on k produces a reducible manifold if and only if k is a (p,q)-cable knot and the surgery slope π equals pq. We extend the work of James Allen Hoffman to prove the Cabling Conjecture for knots with bridge number up to 5.

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