Volume bounds for weaving knots
Abhijit Champanerkar, Ilya Kofman, and Jessica S. Purcell
TL;DR
This paper establishes asymptotically accurate volume bounds for weaving knots, which are a class of alternating knots, and proves that the infinite weave serves as their geometric limit, advancing understanding of their geometric properties.
Contribution
It provides the first asymptotic volume bounds for weaving knots and proves the infinite weave as their geometric limit, addressing conjectures about their maximal volume.
Findings
Established asymptotic volume bounds for weaving knots.
Proved the infinite weave as the geometric limit of weaving knots.
Advanced understanding of the geometric properties of weaving knots.
Abstract
Weaving knots are alternating knots with the same projection as torus knots, and were conjectured by X.-S. Lin to be among the maximum volume knots for fixed crossing number. We provide the first asymptotically correct volume bounds for weaving knots, and we prove that the infinite weave is their geometric limit.
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