ABSTRACT:
(Joint work with Peter Scott)
This talk is about obtaining decompositions for finitely presented
groups which specialize to JSJ-decompositions when restricted to
fundamental groups of Haken 3-manifolds. There have been various such
studies but so far none of them gives the usual JSJ when one
specializes to 3-manifold groups. The new ingradient is the
development of the analogue of regular neighbourhoods for families of
codimension one immersions of groups. The analogue of codimension
one immersion is called almost invariant set and these have been
studied by group theorists since Stallings' work on groups with
infinitely many ends. Recently Peter Scott and I showed (Geometry and
Topology, Vol. 4 (2000), pp 179-218) that many properties of
immersions in low dimensional topology carry over to almost invariant
sets. Concepts and results from this paper will be used.