Journal of Differential Geometry

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 $d ≥ 4$ (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).

Article information

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

Dates
First available in Project Euclid: 20 October 2010

https://projecteuclid.org/euclid.jdg/1287580965

Digital Object Identifier
doi:10.4310/jdg/1287580965

Mathematical Reviews number (MathSciNet)
MR2732977

Zentralblatt MATH identifier
1211.53066

Citation

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. https://projecteuclid.org/euclid.jdg/1287580965