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arXiv · 1810.11512

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

Bruno Duchesne·Robin Tucker-Drob·Phillip Wesolek
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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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Bruno Duchesne, Robin Tucker-Drob, Phillip Wesolek. 2018-10-26. A new lattice invariant for lattices in totally disconnected locally compact groups. https://doi.org/10.1007/s11856-020-2072-2

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