# A construction of pseudo-Anosov homeomorphisms using positive twists

## TL;DR

This paper presents a method to construct pseudo-Anosov homeomorphisms on punctured spheres and higher genus surfaces using positive half-twists, producing examples with diverse algebraic properties of their stretch factors.

## Contribution

It introduces a new construction technique for pseudo-Anosov maps utilizing positive twists, enabling explicit examples with complex number-theoretic features.

## Key findings

- Constructed pseudo-Anosov maps with non-totally real trace fields
- Produced examples with Galois conjugates on the unit circle
- Demonstrated the diversity of algebraic properties in stretch factors

## Abstract

We introduce a construction of pseudo-Anosov homeomorphisms on n-times punctured spheres and surfaces with higher genus using only sufficiently many positive half-twists. These constructions can produce explicit examples of pseudo-Anosov maps with various number-theoretic properties associated to the stretch factors, including examples where the trace field is not totally real and the Galois conjugates of the stretch factor are on the unit circle.