

Knots and Representation Theory
November 13, 2018 18:30, Moscow






Cluster variables on a braid
Seokbeom Yoon^{} 
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Abstract:
Given a braid presentation $D$ of a hyperbolic knot, Hikami and Inoue considered equations arising from a sequence of cluster mutations determined by $D$. They showed that any solution of these equations determines a boundaryparabolic $PSL(2;\mathbb{C})$representation of the knot group. They also conjectured the existence of solution corresponding to the geometric representation. In this talk we will show that a boundaryparabolic representation $\rho$ arises from a solution if and only if the length of $D$ modulo 2 equals the obstruction to lifting $\rho$ to a boundaryparabolic $PSL(2;\mathbb{C})$representation. In particular, the HikamiInoue conjecture holds if and only if the length of $D$ is odd. This work is joint with Jinseok Cho and Christian Zickert.
Language: English

