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

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

2008-12-31

arxiv.org/abs/0901.0056v1

Journal of Differential Geometry 85, no. 2 (2010) pp. 229--270

Mathematics

Geometric Topology

33 pages, 4 figures

Scientific paper

We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension $d$ for all $d\geq 4$. 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.

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