New criteria and constructions of Brunnian links
Sheng Bai, Weibiao Wang
TL;DR
This paper introduces practical methods and criteria for identifying Brunnian links, enabling the creation and detection of such links efficiently, with extensive experiments validating their effectiveness.
Contribution
It provides new practical criteria and a general construction procedure for Brunnian links, applicable to all known examples and enabling bulk creation.
Findings
Methods successfully detect all known Brunnian links
Extensive experiments demonstrate efficiency and practicality
Infinite families of Brunnian links are constructed
Abstract
We present two practical and widely applicable methods, including some criteria and a general procedure, for detecting Brunnian property of a link, if each component is known to be unknot. The methods are based on observation and handwork. They are used successfully for all Brunnian links known so far. Typical examples and extensive experiments illustrate their efficiency. As an application, infinite families of Brunnian links are created, and we establish a general way to construct new ones in bulk
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Taxonomy
TopicsTopological and Geometric Data Analysis · Geometric and Algebraic Topology