Canonical splittings of groups and 3-manifolds

Abstract

We introduce the notion of a 'canonical' splitting over or ℤℤ×ℤ for a finitely generated group G. We show that when G happens to be the fundamental group of an orientable Haken manifold M with incompressible boundary, then the decomposition of the group naturally obtained from canonical splittings is closely related to the one given by the standard JSJ-decomposition of M. This leads to a new proof of Johannson's Deformation Theorem. ©2001 American Mathematical Society.