Hyperbolicity of Brunnian links
Sheng Bai
TL;DR
This paper introduces new geometric and combinatorial methods to establish the hyperbolicity of links, especially Brunnian links, and applies these techniques to classify many known and new hyperbolic Brunnian links.
Contribution
The paper develops novel techniques for proving hyperbolicity of links with unknotted components, extending to all known Brunnian links and discovering new infinite families.
Findings
All known Brunnian links are hyperbolic.
Many infinite families of hyperbolic Brunnian links are identified.
Techniques are broadly applicable to links with unknotted components.
Abstract
We present new techniques to show hyperbolicity of links based on geometric/combinatorial topology. Our techniques are applicable to links that have at least one unknotted component. In particular, they are applicable to Brunnian links. We illustrate our techniques on many examples of Brunnian links. In fact, we determine hyperbolicity for all Brunnian links found in literature. In particular, we discover many infinite families of hyperbolic Brunnian links.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology