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Reducible surgery in lens spaces and seiferters

2015/05/17 by Fyodor Gainullin, Gainullin, Fyodor
Mathematics · Medicine · #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1505.04428

openalex publication_date 2015/05/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The Cabling Conjecture states that surgery on hyperbolic knots in S3 never produces reducible manifolds. In contrast, there do exist hyperbolic knots in some lens spaces with non-prime surgeries. Baker constructed a family of such hyperbolic knots and posed a conjecture that his examples encompass all hyperbolic knots in lens spaces with non-prime surgeries. Using the idea of seiferters we construct a counterexample to this conjecture. In the process of construction, we also derive an obstruction for a small Seifert fibred space to be obtainable by a surgery with a seiferter.

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