Some groups having only elementary actions on metric spaces with hyperbolic boundaries
2004 (English)In: Geometriae Dedicata, ISSN 0046-5755, E-ISSN 1572-9168, Vol. 104, no 1, 119-137 p.Article in journal (Refereed) Published
We study isometric actions of certain groups on metric spaces with hyperbolic-type bordifications. The class of groups considered includes SLn(Z), Artin braid groups and mapping class groups of surfaces (except the lower rank ones). We prove that in various ways such actions must be elementary. Most of our results hold for non-locally compact spaces and extend what is known for actions on proper CAT(- 1) and Gromov hyperbolic spaces. We also show that SLn(Z) for ngreater than or equal to3 cannot act on a visibility space X without. xing a point in (X) over bar. Corollaries concern Floyd's group completion, linear actions on strictly convex cones, and metrics on the moduli spaces of compact Riemann surfaces. Some remarks on bounded generation are also included.
Place, publisher, year, edition, pages
2004. Vol. 104, no 1, 119-137 p.
convergence groups, hyperbolic spaces, mapping class groups, non-locally compact metric spaces, superrigidity, visibility manifolds, commensurators, lattices
IdentifiersURN: urn:nbn:se:kth:diva-23304ISI: 000220672300008OAI: oai:DiVA.org:kth-23304DiVA: diva2:342002
QC 201005252010-08-102010-08-10Bibliographically approved