CAT(0) structures on 3-manifold groups

Hyam Rubinstein

Abstract: This is joint work with Michah Sageev. In Sageev's thesis, it is shown that for a pair consisting of a finitely presented group G and subgroup H, if (G,H) has more than one end, then G acts effectively on a contractible cubical complex X of non positive curvature. If G is the fundamental group of a 3-manifold and H corresponds to an immersed incompressible surface, then we give conditions when the action of G is free and cocompact and X is finite dimensional. In this case, one can view X/G as a blow up of M and there is a natural Cat0 structure on G. In joint work with I. Aitchison, a technique is given for constructing explicit immersed surfaces satisfying the desired properties.

created Thu May 18 15:40:57 PDT 2000