Classification of 3-bridge spheres of 3-bridge arborescent links
Yeonhee Jang
TL;DR
This paper classifies 3-bridge spheres of 3-bridge arborescent links (excluding Montesinos links) by refining existing theorems, and also addresses a question on genus-2 Heegaard splittings of specific graph manifolds.
Contribution
It provides a detailed isotopy classification for 3-bridge spheres of certain arborescent links and refines a theorem relating bridge presentations to Heegaard splittings.
Findings
Classification of 3-bridge spheres for non-Montesinos arborescent links
Refinement of Birman-Hilden theorem on bridge presentations and Heegaard splittings
Answer to Morimoto's question on genus-2 Heegaard splittings of graph manifolds
Abstract
In this paper, we give an isotopy classification of 3-bridge spheres of 3-bridge arborescent links, which are not Montesinos links. To this end, we prove a certain refinement of a theorem of J.S. Birman and H.M. Hilden on the relation between bridge presentations of links and Heegaard splittings of 3-manifolds. In the proof of this result, we also give an answer to a question by K. Morimoto on the classification of genus-2 Heegaard splittings of certain graph manifolds.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Botulinum Toxin and Related Neurological Disorders