Windows, cores and skinning maps

TL;DR

This paper generalizes Thurston's Bounded Image Theorem for skinning maps to a broader class of pared 3-manifolds, exploring properties of divergent sequences and establishing uniform geometric cores.

Contribution

It extends the bounded image theorem to non-acylindrical pared 3-manifolds and analyzes divergence in deformation spaces.

Findings

Generalized Thurston's theorem for a wider class of manifolds

Proved existence of compact cores with uniform geometry

Analyzed properties of divergent sequences in deformation space

Abstract

We give a generalization of Thurston's Bounded Image Theorem for skinning maps, which applies to pared 3-manifolds with incompressible boundary that are not necessarily acylindrical. Along the way we study properties of divergent sequences in the deformation space of such a manifold, establishing the existence of compact cores satisfying a certain notion of uniform geometry.