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

2024/07/13 by Morris, Dave Witte
#06F15 #20F60 #22E40 #37C85 #37E05 #57S25 #Dynamical Systems (math.DS) #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2407.09742

Abstract

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.

Related

• Non left-orderability of lattices in higher rank semi-simple Lie groups
• Bounded generation and lattices that cannot act on the line
• Almost-minimal nonuniform lattices of higher rank
• Higher property T and below-rank phenomena of lattices
• On the profinite rigidity of lattices in higher rank Lie groups