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arXiv:math/0604230 [math.GT]AbstractReferencesReviewsResources

On the Head and the Tail of the Colored Jones Polynomial

Oliver T. Dasbach, Xiao-Song Lin

Published 2006-04-10Version 1

The colored Jones polynomial is a series of one variable Laurent polynomials J(K,n) associated with a knot K in 3-space. We will show that for an alternating knot K the absolute values of the first and the last three leading coefficients of J(K,n) are independent of n when n is sufficiently large. Computation of sample knots indicates that this should be true for any fixed leading coefficient of the colored Jones polynomial for alternating knots. As a corollary we get a Volume-ish Theorem for the colored Jones Polynomial.

Comments: 14 pages, 6 figures
Journal: Compositio Math., Vol 142 (2006), No. 5, pp 1332-1342
Categories: math.GT, math.QA
Subjects: 57M25
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