Turn graphs and extremal surfaces in free groups

TL;DR

This paper offers an alternative explanation of Calegari's rationality theorem concerning stable commutator length in free groups, enhancing understanding of the theorem's implications.

Contribution

It presents a new approach to understanding Calegari's rationality theorem using turn graphs and extremal surfaces in free groups.

Findings

Provides an alternative proof of Calegari's theorem

Clarifies the structure of extremal surfaces in free groups

Enhances conceptual understanding of stable commutator length

Abstract

This note provides an alternate account of Calegari's rationality theorem for stable commutator length in free groups.