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arXiv · 1511.00658

Volume conjecture for $SU(n)$-invariants

Qingtao Chen·Kefeng Liu·Shengmao Zhu
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Abstract

This paper discuss an intrinsic relation among congruent relations \cite{CLPZ}, cyclotomic expansion and Volume Conjecture for $SU(n)$ invariants. Motivated by the congruent relations for $SU(n)$ invariants obtained in our previous work \cite{CLPZ}, we study certain limits of the $SU(n)$ invariants at various roots of unit. First, we prove a new symmetry property for the $SU(n)$ invariants by using a symmetry of colored HOMFLYPT invariants. Then we propose some conjectural formulas including the cyclotomic expansion conjecture and volume conjecture for $SU(n)$ invariants (specialization of colored HOMFLYPT invariants). We also give the proofs of these conjectural formulas for the case of figure-eight knot.

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BibTeXRIS

Qingtao Chen, Kefeng Liu, Shengmao Zhu. 2015-11-02. Volume conjecture for $SU(n)$-invariants. https://arxiv.org/abs/1511.00658

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