The Dehn functions of Out(F_n) and Aut(F_n)

TL;DR

This paper provides a shorter, more direct proof that the Dehn functions of Aut(F_n) and Out(F_n) are exponential for n > 2, confirming their growth rate with improved simplicity.

Contribution

It offers a streamlined proof of the exponential lower bound for Dehn functions of Aut(F_n) and Out(F_n) for n > 4, simplifying previous arguments.

Findings

Dehn functions of Aut(F_n) and Out(F_n) are exponential for n > 2

Previous bounds established exponential growth, with a focus on n=3 and n>4 cases

The paper simplifies the proof of the lower bound for n>4 cases.

Abstract

For n > 2, the Dehn functions of Aut(F_n) and Out(F_n) are exponential. Hatcher and Vogtmann proved that they are at most exponential, and the complementary lower bound in the case n=3 was established by Bridson and Vogtmann. Handel and Mosher completed the proof by reducing the lower bound for n>4 to the case n=3. In this note we give a shorter, more direct proof of this last reduction.