Roushon, S. K. The Farrell-Jones isomorphism conjecture for 3-manifold groups. (English) Zbl 1160.57018 J. \(K\)-Theory 1, No. 1, 49-82 (2008). Let FIC mean the Fibered Isomorphism Conjecture of Farrell and Jones corresponding to the stable topological pseudoisotopy functor (see F. T. Farrell and L. E. Jones [J. Am. Math. Soc. 6, No. 2, 249–297 (1993; Zbl 0798.57018)]). In this fine paper, the author proves that the FIC is true for fundamental groups of a large class of 3-manifolds. He also proves 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 proved by the author which states 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 the FIC for the fundamental group of a graph of groups, where all the vertex and edge groups satisfy the FIC. A consequence of the first result gives a partial solution to a problem in the problem list of R. Kirby [Problems in low-dimensional topology, Providence, RI: American Mathematical Society. AMS/IP Stud. Adv. Math. 2(pt.2), 35–473 (1997; Zbl 0888.57014)]. The author also deduces that the FIC is true for a class of virtually \(PD_3\)-groups. Another main aspect of this paper is to prove the FIC for all Haken 3-manifold groups assuming that the FIC is true for \(B\)-groups. Recall that a group \(G\) is called a \(B\)-group if it contains the fundamental group of a compact orientable irreducible 3-manifold with all the boundary components of higher genus (that is, when the genus is greater than or equal 2) and is incompressible (nonempty) as a subgroup of finite index. Finally, the author proves the FIC for a large class of \(B\)-groups, and moreover, using a recent result of L. E. Jones [A paper for F. T. Farrell on his 60’th birthday, High-dimensional manifold topology, River Edge, NJ: World Scientific. 200–260 (2003; Zbl 1044.57011)], he shows that the surjective part of the FIC is true for any \(B\)-group. Reviewer: Alberto Cavicchioli (Modena) Cited in 12 Documents MSC: 57N37 Isotopy and pseudo-isotopy 19J10 Whitehead (and related) torsion 19D35 Negative \(K\)-theory, NK and Nil Keywords:fibered isomorphism conjecture; fundamental group Citations:Zbl 0798.57018; Zbl 0888.57014; Zbl 1044.57011 PDFBibTeX XMLCite \textit{S. K. Roushon}, J. \(K\)-Theory 1, No. 1, 49--82 (2008; Zbl 1160.57018) Full Text: arXiv