On stable commutator lengths of Dehn twists along separating curves

TL;DR

This paper establishes new upper bounds on the stable commutator lengths of Dehn twists along separating curves in the mapping class group, showing they decrease proportionally to 1 over the genus of the surface.

Contribution

It provides the first explicit bounds of order O(1/g) for these stable commutator lengths, advancing understanding of the algebraic properties of mapping class groups.

Findings

Upper bounds on stable commutator lengths are proportional to 1/g.

Dehn twists along separating curves have bounded stable commutator lengths.

Results improve previous estimates and contribute to geometric group theory.

Abstract

We give new upper bounds on the stable commutator lengths of Dehn twists along separating curves in the mapping class group of a closed oriented surface. The estimates of these upper bounds are $O(1/g)$, where $g$ is the genus of the surface.