Centralizers in Mapping Class Group and decidability of Thurston Equivalence

TL;DR

This paper establishes a constructive bound for centralizers in the Mapping Class Group and proves that Thurston equivalence of certain sphere coverings is algorithmically decidable.

Contribution

It provides a constructive bound for centralizers and demonstrates the decidability of Thurston equivalence for postcritically finite branched coverings.

Findings

Bound for the word length of centralizers

Decidability of Thurston equivalence

Algorithmic approach for sphere coverings

Abstract

We find a constructive bound for the word length of a generating set for the centralizer of an element of the Mapping Class Group. As a consequence, we show that it is algorithmically decidable whether two postcritically finite branched coverings of the sphere are Thurston equivalent.