On Nielsen equivalence classes of two-elements generators of mapping class groups

TL;DR

This paper proves that for surfaces of genus at least eight, the mapping class group has infinitely many Nielsen equivalence classes of two-element generating sets, revealing complex algebraic structure.

Contribution

It establishes the existence of infinitely many Nielsen equivalence classes for two-element generators in high-genus surface mapping class groups, a new insight into their algebraic complexity.

Findings

Infinitely many Nielsen equivalence classes for genus ≥8

Complexity of generating sets in high-genus mapping class groups

New classification results for surface mapping class groups

Abstract

We show that there are infinitely many Nielsen equivalence classes of the mapping class group of a closed oriented surface of genus at least eight.