Geodesic
Volume bounds for weaving knots
Champanerkar, Abhijit1 ; Kofman, Ilya ; Purcell, Jessica2
1Department of Mathematics, College of Staten Island & The Graduate Center, City University of New York, New York, NY 10314, United States
2School of Mathematical Sciences, Monash University, 9 Rainforest Walk, Room 401, Clayton VIC 3800, Australia
Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3301-3323
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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.

DOI : 10.2140/agt.2016.16.3301
Classification : 57M25, 57M50
Keywords: hyperbolic volume, weaving knot, crossing number, geometric limit

Champanerkar, Abhijit  1   ; Kofman, Ilya    ; Purcell, Jessica  2

1 Department of Mathematics, College of Staten Island & The Graduate Center, City University of New York, New York, NY 10314, United States
2 School of Mathematical Sciences, Monash University, 9 Rainforest Walk, Room 401, Clayton VIC 3800, Australia 
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Champanerkar, Abhijit; Kofman, Ilya; Purcell, Jessica. Volume bounds for weaving knots. Algebraic and Geometric Topology, Tome 16 (2016) no. 6, pp. 3301-3323. doi: 10.2140/agt.2016.16.3301

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