5 research outputs found
Vanishing structure set of 3-manifolds
In this short note we update a result proved in [16]. This will complete our
program of [12] showing that the structure set vanishes for compact aspherical
3-manifolds.Comment: 5 pages, referee's suggestions and comments include
The isomorphism conjecture in L-theory
This is the first of three articles on the Fibered Isomorphism Conjecture of
Farrell and Jones for L-theory. We apply the general techniques developed in
[15] and [16] to the L-theory case of the conjecture and prove several results.
Here we prove the conjecture, after inverting 2, for poly-free groups. In
particular, it follows for braid groups. We also prove the conjecture for some
classes of groups without inverting 2. In fact we consider a general class of
groups satisfying certain conditions which includes the above groups and some
other important classes of groups. We check that the properties we defined in
[15] are satisfied in several instances of the conjecture.Comment: 14 pages, AMSLATEX file, the title is revised. item 3 in theorem 1.3
is removed as the proof of this item was found incorrec
The Farrell-Jones isomorphism conjecture for 3-manifold groups
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.Comment: 35 pages, 1 figure (.eps file), AMS Latex file, final version.
accepted for publication in K-theor
Surgery groups of the fundamental groups of hyperplane arrangement complements
Using a recent result of Bartels and Lueck (arXiv:0901.0442) we deduce that
the Farrell-Jones Fibered Isomorphism conjecture in L-theory is true for any
group which contains a finite index strongly poly-free normal subgroup, in
particular, for the Artin full braid groups. As a consequence we explicitly
compute the surgery groups of the Artin pure braid groups. This is obtained as
a corollary to a computation of the surgery groups of a more general class of
groups, namely for the fundamental group of the complement of any fiber-type
hyperplane arrangement in the complex n-space.Comment: 11 pages, AMSLATEX file, revised following referee's comments and
suggestions, to appear in Archiv der Mathemati