Colored Jones polynomials with polynomial growth

Kazuhiro Hikami; Hitoshi Murakami

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arXiv · 0711.2836

Colored Jones polynomials with polynomial growth

Kazuhiro Hikami·Hitoshi Murakami

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Abstract

The volume conjecture and its generalizations say that the colored Jones polynomial corresponding to the N-dimensional irreducible representation of sl(2;C) of a (hyperbolic) knot evaluated at exp(c/N) grows exponentially with respect to N if one fixes a complex number c near 2*Pi*I. On the other hand if the absolute value of c is small enough, it converges to the inverse of the Alexander polynomial evaluated at exp(c). In this paper we study cases where it grows polynomially.

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BibTeX RIS

Kazuhiro Hikami, Hitoshi Murakami. 2008-04-19. Colored Jones polynomials with polynomial growth. https://arxiv.org/abs/0711.2836

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