${rm CAT(0)}$ and ${rm CAT}(-1)$ fillings of hyperbolic manifolds

Koji Fujiwara Tohoku University Jason Fox Manning University at Buffalo

Differential Geometry mathscidoc:1609.10183

Journal of Differential Geometry, 85, (2), 229-269, 2010
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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  title={${rm CAT(0)}$ and ${rm CAT}(-1)$ fillings of hyperbolic manifolds},
  author={Koji Fujiwara, and Jason Fox Manning},
  booktitle={Journal of Differential Geometry},
Koji Fujiwara, and Jason Fox Manning. ${rm CAT(0)}$ and ${rm CAT}(-1)$ fillings of hyperbolic manifolds. 2010. Vol. 85. In Journal of Differential Geometry. pp.229-269. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20160911215845041666840.
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