Non-left-orderability of lattices in higher-rank semisimple Lie groups (after Deroin and Hurtado)
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917721519685632 |
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| author | Morris, Dave Witte |
| author_facet | Morris, Dave Witte |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_09742 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-left-orderability of lattices in higher-rank semisimple Lie groups (after Deroin and Hurtado) Morris, Dave Witte Group Theory Dynamical Systems 20F60, 22E40, 06F15, 37C85, 37E05, 57S25 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. |
| title | Non-left-orderability of lattices in higher-rank semisimple Lie groups (after Deroin and Hurtado) |
| topic | Group Theory Dynamical Systems 20F60, 22E40, 06F15, 37C85, 37E05, 57S25 |
| url | https://arxiv.org/abs/2407.09742 |