Infinite sequence of fixed point free pseudo-Anosov homeomorphisms

TL;DR

This paper constructs infinite sequences of fixed point free pseudo-Anosov homeomorphisms that preserve a sequence of measured foliations, revealing limitations of the Rauzy-Veech induction method in generating such homeomorphisms.

Contribution

It introduces a novel construction of infinite fixed point free pseudo-Anosov homeomorphisms, challenging existing generation techniques.

Findings

Sequences leave invariant a common topological surface and stratum

Demonstrates limitations of Rauzy-Veech induction

Provides explicit examples of fixed point free pseudo-Anosov homeomorphisms

Abstract

We construct infinite sequences of pseudo-Anosov homeomorphisms without fixed points and leaving invariant a sequence of orientable measured foliations on the same topological surface and the same stratum of the space of abelian differentials. The existence of such sequences show that all pseudo-Anosov homeomorphisms fixing orientable measured foliations cannot be obtained by the Rauzy-Veech induction strategy.