Bounded generation and lattices that cannot act on the line
| dc.creator | Lifschitz, Lucy | |
| dc.creator | Morris, Dave Witte | |
| dc.date | 2006-04-28 | |
| dc.date | 2007-06-19 | |
| dc.date.accessioned | 2026-07-07T08:10:54Z | |
| dc.date.available | 2026-07-07T08:10:54Z | |
| dc.description | Let D be an irreducible lattice in a connected, semisimple Lie group G with finite center. Assume that the real rank of G is at least two, that G/D is not compact, and that G has more than one noncompact simple factor. We show that D has no orientation-preserving actions on the real line. (In algebraic terms, this means that D is not right orderable.) Under the additional assumption that no simple factor of G is isogenous to SL(2,R), applying a theorem of E.Ghys yields the conclusion that any orientation-preserving action of D on the circle must factor through a finite, abelian quotient of D. The proof relies on the fact, proved by D.Carter, G.Keller, and E.Paige, that SL(2,A) is boundedly generated by unipotents whenever A is a ring of integers with infinitely many units. The assumption that G has more than one noncompact simple factor can be eliminated if all noncocompact lattices in SL(3,R) and SL(3,C) are virtually boundedly generated by unipotents. | |
| dc.description | 28 pages, no figures. In addition to minor corrections, one result was simplified (and strengthened) because of a stronger result in the final version of a joint paper with V.Chernousov | |
| dc.identifier | https://arxiv.org/abs/math/0604612 | |
| dc.identifier | http://arxiv.org/abs/math/0604612 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/131957 | |
| dc.subject | Group Theory | |
| dc.subject | Geometric Topology | |
| dc.subject | 20F60; 22E40, 57S25 | |
| dc.title | Bounded generation and lattices that cannot act on the line | |
| dc.type | text |