Hadamard spaces with isolated flats
By Christopher Hruska, Bruce Kleiner. 2004
123 citations recorded by the source corpus.
We explore the geometry of nonpositively curved spaces with isolated flats, and its consequences for groups that act properly discontinuously, cocompactly, and isometrically on such spaces. We prove that the geometric boundary of the space is an invariant of the group up to equivariant homeomorphism. We also prove that any such group is relatively hyperbolic, biautomatic, and satisfies the Tits Alternative. The main step in establishing these results is a characterization of spaces with isolated flats as relatively hyperbolic with respect to flats. Finally we show that a CAT(0) space has isolated flats if and only if its Tits boundary is a disjoint union of isolated points and standard Euclidean spheres. In an appendix written jointly with Hindawi, we extend many of the results of this article to a more general setting in which the isolated subspaces are not required to be flats. AMS Classification numbers Primary: 20F67 Secondary: 20F69
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/15f9a167186ba165ad0f6ae77ab6c16480d611c8
How researchers see this paper
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In Geometry and Topology
- Denis V. Osin
- Ashot Minasyan
- D. Groves
- J. Manning
- Goulnara Arzhantseva
- Indira Chatterji
- Kim Ruane
- Alessandro Sisto
In Mathematical Physics
- Denis V. Osin
- D. Groves
- Ashot Minasyan
- J. Manning
- Goulnara Arzhantseva
- Indira Chatterji
- Kim Ruane
- Alessandro Sisto
Citations in the corpus
- Dehn filling in relatively hyperbolic groups (2006, background): “... hyperbolic relative to): (1) Hyperbolic groups are hyperbolic relative to the empty collection of subgroups; (2) Fundamental groups of geometrically finite hyperbolic manifolds are hyperbolic relative to the cusp subgroups; (3) Free products are hyperbolic relative to the free factors; (4) A gro”
- The SQ-universality and residual properties of relatively hyperbolic groups (2006, background): “Groups acting on CAT(0) spaces with isolated flats are hyperbolic relative to the collection of flat stabilizers [13].”
- Some geometric groups with Rapid Decay (2003, methodology): “Recently, Hruska and Kleiner in [ HrK ] extended the work in [Hr1] to all higher dimensions.”
- Limit groups for relatively hyperbolic groups. I. The basic tools (2004, background): “In [28], Hruska and Kleiner prove that if a cocompact CAT.”