Open Access
June 2010 CAT(0) and CAT(−1) fillings of hyperbolic manifolds
Koji Fujiwara, Jason Fox Manning
J. Differential Geom. 85(2): 229-270 (June 2010). DOI: 10.4310/jdg/1287580965


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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Koji Fujiwara. Jason Fox Manning. "CAT(0) and CAT(−1) fillings of hyperbolic manifolds." J. Differential Geom. 85 (2) 229 - 270, June 2010.


Published: June 2010
First available in Project Euclid: 20 October 2010

zbMATH: 1211.53066
MathSciNet: MR2732977
Digital Object Identifier: 10.4310/jdg/1287580965

Rights: Copyright © 2010 Lehigh University

Vol.85 • No. 2 • June 2010
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