Abstract

The connectivity locus $M$ for 2-gon complex trees $T{c,-c}$ turns out to be the closure of all roots (contained in the unit disk) of polynomials with coefficients 1, -1, and 0, starting always with 1. If we select only roots of polynomials with coefficients equal to 1 or -1 then we obtain a subset $M_0$ which is tightly connected to the Thurston Set introduced in Bill Thurston’s last paper "Entropy in Dimension One". In this talk we will explore the internal structure of $M$ that follows naturally from the node-to-node connectivity theorem of 2-gon complex trees $T{c,-c}$.