Volume 16, issue 6 (2016)

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ISSN (electronic): 1472-2739
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Volume bounds for weaving knots

Abhijit Champanerkar, Ilya Kofman and Jessica S Purcell

Algebraic & Geometric Topology 16 (2016) 3301–3323
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