Geodesic
On links with cyclotomic Jones polynomials
Champanerkar, Abhijit1 ; Kofman, Ilya2
1Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA
2Department of Mathematics, College of Staten Island, City University of New York, 2800 Victory Boulevard, Staten Island, NY 10314, USA
Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1655-1668
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We show that if {Ln} is any infinite sequence of links with twist number τ(Ln) and with cyclotomic Jones polynomials of increasing span, then limsupτ(Ln) = ∞. This implies that any infinite sequence of prime alternating links with cyclotomic Jones polynomials must have unbounded hyperbolic volume. The main tool is the multivariable twist–bracket polynomial, which generalizes the Kauffman bracket to link diagrams with open twist sites.

DOI : 10.2140/agt.2006.6.1655
Keywords: Jones polynomial, Mahler measure, twist sites, hyperbolic volume

Champanerkar, Abhijit  1   ; Kofman, Ilya  2

1 Department of Mathematics and Statistics, University of South Alabama, Mobile, AL 36688, USA
2 Department of Mathematics, College of Staten Island, City University of New York, 2800 Victory Boulevard, Staten Island, NY 10314, USA 
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Champanerkar, Abhijit; Kofman, Ilya. On links with cyclotomic Jones polynomials. Algebraic and Geometric Topology, Tome 6 (2006) no. 4, pp. 1655-1668. doi: 10.2140/agt.2006.6.1655

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