Volume bounds for weaving knots

Champanerkar, Abhijit; Kofman, Ilya; Purcell, Jessica

doi:10.2140/agt.2016.16.3301

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Volume bounds for weaving knots

Abhijit Champanerkar, Ilya Kofman and Jessica S Purcell

Algebraic & Geometric Topology 16 (2016) 3301–3323

DOI: 10.2140/agt.2016.16.3301

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 sharp volume bounds for weaving knots, and we prove that the infinite square weave is their geometric limit.

Keywords

hyperbolic volume, weaving knot, crossing number, geometric limit

Mathematical Subject Classification 2010

Primary: 57M25, 57M50

References

Publication

Received: 19 June 2015

Revised: 23 May 2016

Accepted: 9 June 2016

Published: 15 December 2016

Authors

Abhijit Champanerkar
Department of Mathematics College of Staten Island & The Graduate Center City University of New York New York, NY 10314 United States

Ilya Kofman


Jessica S Purcell
School of Mathematical Sciences Monash University 9 Rainforest Walk, Room 401 Clayton VIC 3800 Australia

Volume 16, issue 6 (2016)