Article

# The fibered isomorphism conjecture for complex manifolds

(Impact Factor: 0.48). 09/2002; 23(4). DOI: 10.1007/s10114-005-0759-2
Source: arXiv

ABSTRACT

In this paper we show that the Fibered Isomorphism Conjecture of Farrell and Jones, corresponding to the stable topological pseudoisotopy functor, is true for the fundamental groups of a class of complex manifolds. A consequence of this result is that the Whitehead group, reduced projective class groups and the negative K-groups of the fundamental groups of these manifolds vanish whenever the fundamental group is torsion free. We also prove the same results for a class of real manifolds including a large class of 3-manifolds which has a finite sheeted cover fibering over the circle.

### Full-text preview

Available from: ArXiv
• Source
##### Article: K-theory of virtually poly-surface groups
[Hide abstract]
ABSTRACT: In this paper we generalize the notion of strongly poly-free group to a larger class of groups, we call them strongly poly-surface groups and prove that the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor is true for any virtually strongly poly-surface group. A consequence is that the Whitehead group of a torsion free subgroup of any virtually strongly poly-surface group vanishes.
Algebraic & Geometric Topology 10/2002; 3(1). DOI:10.2140/agt.2003.3.103 · 0.45 Impact Factor
• Source
##### Article: Erratum to “K–theory of virtually poly-surface groups”
[Hide abstract]
ABSTRACT: In this note, we point out an error in the above paper. We also refer to some papers where this error is corrected partially and describe a positive approach to correct it completely. AMS Classification 57N37, 19J10; 19D35
Algebraic & Geometric Topology 08/2004; 3(2):1291-1292. DOI:10.2140/agt.2003.3.1291 · 0.45 Impact Factor
• Source
##### Article: The Farrell-Jones isomorphism conjecture for 3-manifold groups
[Hide abstract]
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.
Journal of K-theory K-theory and its Applications to Algebra Geometry and Topology 05/2004; 1(1). DOI:10.1017/is007011012jkt005 · 0.69 Impact Factor