Stable specific torsion length and periodic mapping classes

TL;DR

This paper investigates properties of periodic mapping classes, introducing the stable specific torsion length concept and establishing bounds for Dehn twists, advancing understanding of their algebraic and geometric structure.

Contribution

It introduces the stable specific torsion length for group elements and proves an upper bound for Dehn twists, linking geometric actions to algebraic invariants.

Findings

Existence of a power of any periodic mapping class that maps a nonseparating curve to a disjoint one

Definition of stable specific torsion length for group elements

Bound of six for the stable specific torsion length of a Dehn twist

Abstract

We show that for any periodic mapping class, there is some power which maps a nonseparating, simple closed curve to a distinct, disjoint nonseparating curve. As an application of this result, we introduce the notion of stable specific torsion length of a group element and show that the stable specific torsion length of a Dehn twist is bounded above by six.