Journal of Differential Geometry

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

Koji Fujiwara and Jason Fox Manning

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We give new examples of hyperbolic and relatively hyperbolic groups of cohomological dimension $d$ for all $d ≥ 4$ (see Theorem 2.13). 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 (see Section 5).

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J. Differential Geom., Volume 85, Number 2 (2010), 229-270.

First available in Project Euclid: 20 October 2010

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Fujiwara, Koji; Manning, Jason Fox. CAT(0) and CAT(−1) fillings of hyperbolic manifolds. J. Differential Geom. 85 (2010), no. 2, 229--270. doi:10.4310/jdg/1287580965.

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