Action Dimension of Lattices in Euclidean Buildings

Kevin Schreve

doi:10.2140/agt.2018.18.3257

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arXiv · 1703.00616

Action Dimension of Lattices in Euclidean Buildings

Kevin Schreve

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Abstract

The action dimension of a group G is the minimal dimension of a contractible manifold that G acts on properly discontinuously. We show that if G acts properly and cocompactly on a thick Euclidean building, then the action dimension is bounded below by twice the dimension of the building. We also compute the action dimension of S-arithmetic groups over number fields, partially answering a question of Bestvina, Kapovich, and Kleiner.

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Kevin Schreve. 2017-03-02. Action Dimension of Lattices in Euclidean Buildings. https://doi.org/10.2140/agt.2018.18.3257

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