Abstract
To a knot in –space, one can associate a sequence of Laurent polynomials, whose –th term is the –th colored Jones polynomial. The paper is concerned with the asymptotic behavior of the value of the –th colored Jones polynomial at , when is a fixed complex number and tends to infinity. We analyze this asymptotic behavior to all orders in when is a sufficiently small complex number. In addition, we give upper bounds for the coefficients and degree of the –th colored Jones polynomial, with applications to upper bounds in the Generalized Volume Conjecture. Work of Agol, Dunfield, Storm and W Thurston implies that our bounds are asymptotically optimal. Moreover, we give results for the Generalized Volume Conjecture when is near . Our proofs use crucially the cyclotomic expansion of the colored Jones function, due to Habiro.
Citation
Stavros Garoufalidis. Thang T Q Lê. "Asymptotics of the colored Jones function of a knot." Geom. Topol. 15 (4) 2135 - 2180, 2011. https://doi.org/10.2140/gt.2011.15.2135
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