Asymptotics of the colored Jones function of a knot
By Stavros Garoufalidis, Thang T. Q. Lê. 2005
61 citations recorded by the source corpus.
To a knot in 3-space, one can associate a sequence of Laurent polynomials, whose nth term is the nth colored Jones polynomial. The paper is concerned with the asymptotic behavior of the value of the nth colored Jones polynomial at e�/n, whenis a fixed complex number and n tends to infinity. We analyze this asymptotic behavior to all orders in 1/n whenis a sufficiently small complex number. In addition, we give upper bounds for the coefficients and degree of thenth colored Jones polynomial, with applications to upper bounds in the Generalized Volume Conjecture. Work of Agol-Dunfield-Storm-W.Thurston implies that our bounds are asymptotically optimal. Moreover, we give results for the Generalized Volume Conjecture when � is near 2�i. Our proofs use crucially the cyclotomic expansion of the colored Jones function, due to Habiro.
Subfields: Computational Theory and Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/6e0dd3dbd748eba73b4338030e664e302eaecdae
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In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
In Geometry and Topology
Citations in the corpus
- Analytic Continuation Of Chern-Simons Theory (2010, background): “Moreover [9], in the semiclassical limit, Jn(q) is bounded as n→ ∞ for sufficiently small γ.”