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Caprace, Pierre-Emmanuel; Sageev, Michah (2010)
Languages: English
Types: Preprint
Subjects: 20F65, 20F67, 53C21, Mathematics - Group Theory

Classified by OpenAIRE into

arxiv: Mathematics::Metric Geometry
We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube complex contains a rank one isometry. This implies that the Rank Rigidity Conjecture holds for CAT(0) cube complexes. We derive a number of other consequences for CAT(0) cube complexes, including a purely geometric proof of the Tits Alternative, an existence result for regular elements in (possibly non-uniform) lattices acting on cube complexes, and a characterization of products of trees in terms of bounded cohomology.
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