Lower Bound For Dilatations

TL;DR

This paper establishes a new polynomial lower bound for the dilatation of pseudo-Anosov maps on surfaces, improving upon previous super-exponential bounds in terms of genus.

Contribution

It introduces a significantly improved lower bound for dilatations, reducing the dependence from super-exponential to polynomial in genus.

Findings

New polynomial lower bound for dilatations

Improved understanding of pseudo-Anosov map dynamics

Enhanced bounds applicable to surfaces with punctures

Abstract

We prove a new lower bound for the dilatation of an arbitrary pseudo-Anosov map on a surface of genus g with n punctures. Our bound improves the former super-exponential dependence on the genus by a polynomial dependence.