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Relatively geometric
actions of Kähler groups on $\mathrm{CAT}(0)$ cube
complexes
Corey Bregman, Daniel Groves and Kejia Zhu |
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Algebraic & Geometric Topology 24 (2024) 4127–4137
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Abstract |
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We prove that for , a nonuniform lattice in does not admit a relatively geometric action on a cube complex. As a consequence, if is a nonuniform lattice in a noncompact semisimple Lie group without compact factors that admits a relatively geometric action on a cube complex, then is commensurable with . We also prove that if a Kähler group is hyperbolic relative to residually finite parabolic subgroups, and acts relatively geometrically on a cube complex, then it is virtually a surface group. |
Keywords
CAT(0) cube complexes, relatively hyperbolic groups,
complex hyperbolic lattices, toroidal compactification
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Mathematical Subject Classification
Primary: 20F65, 22E40
Secondary: 32J05, 32J27, 57N65
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References |
Publication
Received: 21 August 2023
Revised: 5 January 2024
Accepted: 31 January 2024
Published: 9 December 2024
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Authors |
| Corey Bregman | |
| Department of Mathematics Tufts University Medford, MA United States |
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| https://sites.google.com/view/cbregman | |
| Daniel Groves | |
| Department of Mathematics,
Statistics and Computer Science University of Illinois at Chicago Chicago, IL United States |
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| http://homepages.math.uic.edu/~groves/ | |
| Kejia Zhu | |
| Department of Mathematics University of California at Riverside Riverside, CA United States |
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| https://sites.google.com/view/kejiazhu | |
| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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