Constructing pseudo-Anosov maps with given dilatations

TL;DR

This paper provides conditions under which a Perron number can serve as a pseudo-Anosov dilatation and offers an explicit construction of the corresponding surface and map.

Contribution

It introduces sufficient conditions for Perron numbers to be pseudo-Anosov dilatations and constructs explicit examples when these conditions are satisfied.

Findings

Identifies sufficient conditions for Perron numbers to be pseudo-Anosov dilatations

Provides explicit constructions of surfaces and maps under these conditions

Enhances understanding of the relationship between Perron numbers and pseudo-Anosov maps

Abstract

In this paper, we give sufficient conditions for a Perron number, given as the leading eigenvalue of an aperiodic matrix, to be a pseudo-Anosov dilatation of a compact surface. We give an explicit construction of the surface and the map when the sufficient condition is met.