Title: **The Farrell-Jones isomorphism conjecture
for
3-manifold
groups** (accepted for publication in K-theory, later shifted
and appeared in Journal of K-theory)

Abstract: *We show that
the Fibered Isomorphism Conjecture (FIC) of Farrell and Jones
corresponding to the stable topological pseudoisotopy functor is true
for the fundamental groups of a large class of 3-manifolds. We also
prove that if the FIC is true for irreducible
3-manifold groups then it is true for all 3-manifold groups. In fact,
this follows
from a more general result we prove here, namely we show that if the
FIC is true for each vertex group of a graph of groups with trivial
edge groups then the FIC is true for the fundamental group of the graph
of groups. This result is part of a program to prove FIC for the
fundamental group of a graph of groups where all the vertex and edge
groups satisfy FIC. A consequence of the first result gives a partial
solution to a problem in the problem list of R. Kirby. We also deduce
that the FIC is true for a class of virtually PD_3-groups.
Another main aspect of this article is to prove the FIC for all Haken
3-manifold groups assuming that the FIC is true for B-groups. By
definition a B-group contains a finite index subgroup isomorphic to the
fundamental group of a compact irreducible 3-manifold with
incompressible nonempty boundary so that each boundary component is of
genus \geq 2. We also prove the FIC for a large class of B-groups and
moreover, using a recent result of L.E. Jones we show that the
surjective part of the FIC is true for
any B-group.*