Lyapunov spectrum of ball quotients with applications to commensurability questions

TL;DR

This paper calculates the Lyapunov spectrum of certain ball quotients from cyclic coverings, using intersection theory and period map analysis, leading to a classification of their commensurability classes.

Contribution

It provides a novel method to compute Lyapunov spectra for ball quotients and completes the classification of their commensurability classes.

Findings

Lyapunov spectrum of specific ball quotients determined

Classification of non-arithmetic ball quotient classes completed

Method involves intersection numbers and boundary analysis

Abstract

We determine the Lyapunov spectrum of ball quotients arising from cyclic coverings. The computations are performed by rewriting the sum of Lyapunov exponents as ratios of intersection numbers and by the analysis of the period map near boundary divisors. As a corollary, we complete the classification of commensurability classes of all presently known non-arithmetic ball quotients.