The quadratic isoperimetric inequality for mapping tori of free group automorphisms I: Positive automorphisms

TL;DR

This paper proves that for finitely generated free groups with positive automorphisms, the associated mapping tori satisfy a quadratic isoperimetric inequality, advancing understanding of their geometric properties.

Contribution

It establishes a quadratic isoperimetric inequality for mapping tori of free groups under positive automorphisms, a significant step in geometric group theory.

Findings

Mapping tori of free groups with positive automorphisms satisfy quadratic isoperimetric inequalities.

The result applies to finitely generated free groups and their automorphisms.

Provides foundational results for further studies in geometric properties of automorphisms.

Abstract

If $F$ is a finitely generated free group and $\phi$ is a positive automorphism of $F$ then $F\rtimes_\phi Z$ satisfies a quadratic isoperimetric inequality.