Virtual homological spectral radii for automorphisms of surfaces

TL;DR

This paper proves that surface automorphisms with positive entropy always have a virtual homological eigenvalue outside the unit circle, linking dynamical complexity to algebraic properties.

Contribution

It establishes a new connection between surface automorphisms' entropy and their virtual homological eigenvalues, advancing understanding of surface dynamics.

Findings

Automorphisms with positive entropy have virtual homological eigenvalues outside the unit circle.

The result links dynamical entropy to algebraic spectral properties.

Provides new insights into the structure of surface automorphisms.

Abstract

In this paper, it is shown that any surface automorphism of positive mapping-class entropy possesses a virtual homological eigenvalue which lies outside the unit circle of the complex plane.