Cannon-Thurston Maps for Surface Groups I: Amalgamation Geometry and Split Geometry

Abstract

We introduce the notion of manifolds of amalgamation geometry and its generalization, split geometry. We show that the limit set of any surface group of split geometry is locally connected, by constructing a natural Cannon-Thurston map.

v 5: 73 pages, 7 figures. References updated. Subsection on partial electrocution modified. Introductory comments added

References in corpus (1)

• Cannon-Thurston Maps for Pared Manifolds of Bounded Geometry

Cited by in corpus (2)

• Cannon-Thurston Maps for Pared Manifolds of Bounded Geometry
• Geometrically finite and infinite Kleinian Groups