Quasi-isometry of graph manifold groups and Artin groups

Geometry & Topology
Event time: 
Tuesday, April 18, 2006 - 12:30pm to Monday, April 17, 2006 - 8:00pm
431 DL
Walter Neumann
Speaker affiliation: 
Columbia University
Event description: 

Joint work with Behrstock. We classify the fundamental groups of non-geometric compact graph manifolds up to quasi-isometry. For closed graph manifolds there is just one QI class, answering a question of Kapovitch and Leeb. For graph manifolds with non-empty boundary the number of QI classes is infinite, although it is finite if one bounds the number of geometric components in the JSJ decomposition. For example, there are exactly 2921253 QI classes for graph-manifolds with at most seven geometric components; in contrast, the number of commensurability classes is infinite already for graph manifolds with one geometric component. Applications to QI classification of certain Artin groups (eg, those whose Artin graph is a tree), will also be described.