Tightness and efficiency of irreducible automorphisms of handlebodies II

TL;DR

This paper completes the proof that irreducible automorphisms of handlebodies are efficient if and only if their associated invariant laminations are geometrically tight, establishing a precise criterion for efficiency.

Contribution

It proves the converse of a previous result, showing that geometric tightness of invariant laminations characterizes efficiency of automorphisms of handlebodies.

Findings

Efficiency of automorphisms is equivalent to geometric tightness of laminations.

The paper completes the characterization of automorphism efficiency.

Provides a criterion for analyzing automorphisms of handlebodies.

Abstract

We finish proving that an irreducible automorphism f of a handlebody is efficient if, and only if, a certain standard pair of dual f--invariant laminations have the geometric tightness property. In a previous paper it was proved that this tightness property implies efficiency. We now prove the converse.