Actions of lattices in $S$-arithmetic groups on manifolds

Segev Gonen Cohen

Actions of lattices in $S$-arithmetic groups on manifolds

Dynamical Systems 2026-07-01 v1 Group Theory Geometric Topology

Authors: Segev Gonen Cohen

Abstract

We prove that an action by $C^1$ diffeomorphisms of a lattice in a simple $p$ -adic group on a compact manifold is finite, provided the dimension is less than the rank. We extend this statement to lattices in totally disconnected $S$ -arithmetic groups, where the critical dimension is the maximal rank of the simple factors. This uses the machinery developed by Brown, Fisher, and Hurtado.

Keywords

lattice actions S-arithmetic groups p-adic groups compact manifolds C1 diffeomorphisms critical dimension

Cite

@article{arxiv.2607.00697,
  title  = {Actions of lattices in $S$-arithmetic groups on manifolds},
  author = {Segev Gonen Cohen},
  journal= {arXiv preprint arXiv:2607.00697},
  year   = {2026}
}

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