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arxiv: 2407.09742 · v1 · pith:VWXZQZPQ · submitted 2024-07-13 · math.GR · math.DS

Non-left-orderability of lattices in higher-rank semisimple Lie groups (after Deroin and Hurtado)

Dave Witte Morris This is my paper

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classification math.GR math.DS
keywords realsemisimpleadicderoingroupshurtadolatticelattices
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Let $G$ be a connected, semisimple, real Lie group with finite centre, with real rank at least two. B.Deroin and S.Hurtado recently proved the 30-year-old conjecture that no irreducible lattice in $G$ has a left-invariant total order. (Equivalently, they proved that no such lattice has a nontrivial, orientation-preserving action on the real line.) We will explain many of the main ideas of the proof, by using them to prove the analogous result for lattices in $p$-adic semisimple groups. The $p$-adic case is easier, because some of the technical issues do not arise.

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