Volume bounds for 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.

17 pages, 12 figures. Formerly part of arXiv:1411.7915. V2: minor corrections in sections 2 and 4; clarified and expanded exposition throughout

Cited by in corpus (12)

• Geometry of biperiodic alternating links
• Right-angled polyhedra and alternating links
• Mahler Measure and the Vol-Det Conjecture
• Determinant density and biperiodic alternating links
• Alternating links with totally geodesic checkerboard surfaces
• Alternating links on surfaces and volume bounds
• Density spectra for knots
• A survey of hyperbolic knot theory
• The Determinant and Volume of 2-Bridge Links and Alternating 3-Braids
• Minimal 4-colored graphs representing an infinite family of hyperbolic 3-manifolds
• The Jones Polynomial and Khovanov Homology of Weaving Knots $W(3,n)$
• Generalized bipyramids and hyperbolic volumes of tiling links