Root laminations of arbitrary degree

TL;DR

This paper introduces a canonical method to associate invariant q-laminations with degree d critical portraits, advancing the classification of such laminations in complex dynamics.

Contribution

It provides a systematic construction linking critical portraits to invariant q-laminations for any degree d, aiding classification efforts.

Findings

Established a canonical association between critical portraits and q-laminations.

Laid groundwork for classifying all degree d invariant q-laminations.

Extended the theory of geodesic laminations in complex dynamics.

Abstract

This paper studies the space of degree $d>1$ invariant q-laminations, i.e., geodesic laminations invariant under the $d$-tupling map of the circle and associated with equivalence relations. Our main construction associates a q-lamination with any degree $d$ critical portrait \emph{in a canonical way}. Even though somewhat technical, this is the initial step in the program of classification of all degree $d$ invariant q-laminations.