Groups acting on tree-graded spaces
by
Mark Sapir
Vanderbilt University
Coauthors: Cornelia Druţu

We develop a theory of groups acting on tree-graded spaces

generalizing the Rips-Bestvina-Feighn-Sela theory of groups acting on R-trees.

Tree-graded spaces appear as asymptotic cones of a wide class of groups

including mapping class groups, fundamental groups of graph manifolds,

geometrically finite Kleinian groups and relatively hyperbolic groups in

general. Our results allow us to describe relatively hyperbolic groups G

with infinite Out(G) (generalizing results of Rips-Sela's and others), and

establish results about splittings of groups with infinitely many

homomorphisms into a relatively hyperbolic groups.

Date received: March 21, 2006