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A new lattice invariant for lattices in totally disconnected locally compact groups

Abstract : We introduce and explore a natural rank for totally disconnected locally compact groups called the bounded conjugacy rank. This rank is shown to be a lattice invariant for lattices in sigma compact totally disconnected locally compact groups; that is to say, for a given sigma compact totally disconnected locally compact group, some lattice has bounded conjugacy rank n if and only if every lattice has bounded conjugacy rank n. Several examples are then presented.
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https://hal.archives-ouvertes.fr/hal-01916002
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Submitted on : Thursday, November 8, 2018 - 10:44:17 AM
Last modification on : Wednesday, November 3, 2021 - 8:08:42 AM
Long-term archiving on: : Saturday, February 9, 2019 - 1:00:37 PM

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Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek. A new lattice invariant for lattices in totally disconnected locally compact groups. Israël Journal of Mathematics, Hebrew University Magnes Press, 2020, 240, pp.539-565. ⟨10.1007/s11856-020-2072-2⟩. ⟨hal-01916002⟩

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