Alex Eskin : Quasi-isometries and rigidity of solvable groups

Posted by Dhruv Mubayi , part of the Departmental Colloquium.

At

Oct. 13, 2006, 3 p.m.

In

SEO 636

Abstract

The notion of quasi-isometry is the natural equivalence relation if one views groups as metric spaces. We prove that any group quasi-isometric to the three dimenionsional solvable Lie group Sol is virtually a lattice in Sol. Our results extend to some other classes of groups and spaces, and are contributions to Gromov's program for classifying finitely generated groups up to quasi-isometry [Gr2]. We introduce a new technique for studying quasi-isometries, which we refer to as "coarse differentiation". This is joint work with David Fisher and Kevin Whyte.