Rank Rigidity for Cat(0) Cube Complexes |
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Authors: | Pierre-Emmanuel Caprace Michah Sageev |
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Institution: | 1. UCLouvain ?C IRMP, Chemin du Cyclotron 2, 1348, Louvainla-Neuve, Belgium 2. Department of Mathematics, Technion, Haifa, 32000, Israel
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Abstract: | We prove that any group acting essentially without a fixed point at infinity on an irreducible finite-dimensional CAT(0) cube
complex contains a rankone 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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Keywords: | |
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