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

Mathematics – Geometric Topology

Scientific paper

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

Scientific paper

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.

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