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

Abstract: This article has two
purposes. In [1] we showed that
the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for
a particular class of 3-manifolds (we denoted this class by \cal
C) is the key to prove the FIC for 3-manifold groups in general. And we
proved the FIC for the fundamental groups of members of a subclass of
\cal C. This result was obtained by showing that the double of any
member of this subclass is either Seifert fibered or supports a
nonpositively curved metric. In this article we prove that for any M in
\cal C there is a closed 3-manifold P such that either P is Seifert
fibered or is a nonpositively curved
3-manifold and \pi_1(M) is a subgroup of \pi_1(P). As a consequence
this proves that the FIC is true for any B-group (see definition 3.2 in
[1]). Therefore, the FIC is true for
any Haken 3-manifold group and hence for any 3-manifold group (using
the reduction theorem of [1])
provided we assume the Geometrization conjecture. The above result also
proves the FIC for a class of 4-manifold groups (see [12]).

The second aspect of this article is to relax a condition in the
definition of strongly
poly-surface group ([9]) and define
a
new class of groups (we call them weak strongly poly-surface
groups). Then using the above result we prove the FIC for any virtually
weak strongly
poly-surface group. We also give a corrected proof
of the main lemma of [9].