Canonical Thurston Obstructions for Sub-Hyperbolic Semi-Rational Branched Coverings

TL;DR

This paper establishes the existence of canonical Thurston obstructions in sub-hyperbolic semi-rational branched coverings when they are not equivalent to rational maps, advancing understanding in complex dynamics.

Contribution

It proves the existence of canonical Thurston obstructions for a class of branched coverings, clarifying conditions for rational map equivalence.

Findings

Canonical Thurston obstructions exist for non-equivalent cases.

Provides criteria distinguishing rational maps from other branched coverings.

Enhances theoretical framework in complex dynamics and branched covering classification.

Abstract

We prove that the canonical Thurston obstruction for a sub-hyperbolic semi-rational branched covering exists if the branched covering is not CLH-equivalent to a rational map.