A family of pseudo-Anosov braids whose super summit sets grow exponentially

TL;DR

This paper demonstrates that the super summit set size of pseudo-Anosov braids can grow exponentially with their canonical length, revealing new complexity in braid group dynamics.

Contribution

It proves that the super summit set size can grow exponentially for pseudo-Anosov braids, a previously unknown growth behavior.

Findings

Super summit set size grows exponentially with canonical length

Exponential growth occurs even for pseudo-Anosov braids

Provides new insights into braid group complexity

Abstract

We prove that the size of the super summit set of a braid can grow exponentially with the canonical length of the braid, even for pseudo-Anosov braids.