Low dilatation pseudo-Anosovs on punctured surfaces and volume

Abstract

For a pseudo-Anosov homeomorphism $f$ on a closed surface of genus $g\ge 2$, for which the entropy is on the order $\frac{1}{g}$ (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of $g$. We show that the analogous result fails for a surface of fixed genus $g$ with $n$ punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order $\frac{\log n}{n}$, and volume tending to infinity.

18 pages, 11 figures

References in corpus (1)

• A family of pseudo-Anosov braids with small dilatation