### The quadratic isoperimetric inequality for mapping tori of free-group automorphisms

#### This is a monograph in 3 parts. The 3 parts have circulated individually in recent years. This final version of the manuscript was delivered on 8 Feb 2008.

If $F$ is a finitely generated free group and $\phi$ is an automorphism, then the Dehn function of $F\rtimes_\phi\Bbb Z$ is either linear or quadratic.