CAT(0) and CAT(-1) fillings of hyperbolic manifolds

Abstract

We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension $d$ for all $d\ge 4$. These examples result from applying CAT$(0)$/CAT$(-1)$ filling constructions (based on singular doubly warped products) to finite volume hyperbolic manifolds with toral cusps. The groups obtained have a number of interesting properties, which are established by analyzing their boundaries at infinity by a kind of Morse-theoretic technique, related to but distinct from ordinary and combinatorial Morse theory.

33 pages, 4 figures

References in corpus (4)

• Limit groups for relatively hyperbolic groups, II: Makanin-Razborov diagrams
• Completion of the Proof of the Geometrization Conjecture
• Volume change under drilling
• Complex hyperbolic hyperplane complements

Cited by in corpus (1)

• All finitely presentable groups from link complements and Kleinian groups