Extending pseudo-Anosov maps to compression bodies

TL;DR

This paper characterizes when pseudo-Anosov maps on boundary components of 3-manifolds extend into the interior, linking this to lamination limits and using hyperbolic geometry and algebraic limits of convex cocompact compression bodies.

Contribution

It provides a new criterion for extending pseudo-Anosov maps into the interior of 3-manifolds based on lamination limits and hyperbolic geometric analysis.

Findings

A pseudo-Anosov map extends partially into the interior iff its lamination is a projective limit of meridians.

The proof involves analyzing algebraic limits of convex cocompact compression bodies.

The work connects lamination theory with hyperbolic geometry in 3-manifold topology.

Abstract

We show that a pseudo-Anosov map on a boundary component of an irreducible 3-manifold has a power that partially extends to the interior if and only if its (un)stable lamination is a projective limit of meridians. The proof is through 3-dimensional hyperbolic geometry, and involves an investigation of algebraic limits of convex cocompact compression bodies.