Geodesic
Action dimension of lattices in Euclidean buildings
Schreve, Kevin1
1 Department of Mathematics, University of Michigan, Ann Arbor, MI, United States
Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3257-3277

Voir la notice de l'article provenant de la source Mathematical Sciences Publishers

We show that if a discrete group Γ acts properly and cocompactly on an n–dimensional, thick, Euclidean building, then Γ cannot act properly on a contractible (2n−1)–manifold. As an application, if Γ is a torsion-free S–arithmetic group over a number field, we compute the minimal dimension of contractible manifold that admits a proper Γ–action. This partially answers a question of Bestvina, Kapovich, and Kleiner.

DOI : 10.2140/agt.2018.18.3257
Classification : 20F36, 20F65, 20F55, 57Q35, 20J06
Keywords: action dimension, Euclidean building, S-arithmetic group, van Kampen obstruction

Schreve, Kevin 1

1 Department of Mathematics, University of Michigan, Ann Arbor, MI, United States 
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Schreve, Kevin. Action dimension of lattices in Euclidean buildings. Algebraic and Geometric Topology, Tome 18 (2018) no. 6, pp. 3257-3277. doi: 10.2140/agt.2018.18.3257

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