On links with cyclotomic Jones polynomials

Abhijit Champanerkar; Ilya Kofman

doi:10.2140/agt.2006.6.1655

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On links with cyclotomic Jones polynomials

Abhijit Champanerkar·Ilya Kofman

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Abstract

We show that if {L_n} is any infinite sequence of links with twist number tau(L_n) and with cyclotomic Jones polynomials of increasing span, then lim sup tau(L_n)=infty. 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.

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BibTeX RIS

Abhijit Champanerkar, Ilya Kofman. 2009-04-30. On links with cyclotomic Jones polynomials. https://doi.org/10.2140/agt.2006.6.1655

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