L2-invariants and negatively curved groups

Abstract: I present results about the structure of a wide class of infinite groups which were obtained in collaboration with Jesse Peterson (Berkeley). Using L2-cohomology we obtained strong results about the subgroup structure of groups with positive first L2 Betti number. Moreover, some results extend to other classes of groups with weaker negative curvature properties (like hyperbolic groups). The results generalize several central results in geometric and combinatorial group theory.