Commensurability of two-multitwist pseudo-Anosovs

TL;DR

This paper investigates the relationships between certain surface automorphisms generated by two Dehn multitwists, exploring their commensurability, invariants, and constructing infinite classes of related pseudo-Anosov homeomorphisms.

Contribution

It provides new results on noncommensurability among classes from canonical curves and introduces a general method to construct infinite commensurable classes.

Findings

Pairwise noncommensurability between classes from canonical curve configurations.

Analysis of the Kenyon-Smillie invariant J for these flat surfaces.

A new construction method for infinite classes of commensurable pseudo-Anosov homeomorphisms.

Abstract

This paper analyzes commensurability of the class of surface automorphism generated by two Dehn multitwists. We show pairwise noncommensurability between several classes arising from canonical curve configurations. In addition, we consider the Kenyon-Smillie invariant J of flat surfaces in this setting. We also introduce a general construction of infinite classes of commensurable pseudo-Anosov homeomorphisms.