Standardly embedded train tracks and pseudo-Anosov maps with minimum expansion factor

Abstract

We show that given a fully punctured pseudo-Anosov map $f:S\to S$ whose punctures lie in at least two orbits under the action of $f$, the expansion factor $\lambda (f)$ satisfies the inequality

where $\mu =\frac{1+\sqrt{5}}{2}\approx 1.61803$ is the golden ratio. The proof involves a study of standardly embedded train tracks, and the Thurston symplectic form defined on their weight space.