Three-manifolds with fundamental group a free product

Manifolds with Fundamental Group a Generalized Free Product. I

This announcement describes new methods in the study and classification of differentiable, PI or topological manifolds with infinite fundamental group. If, for example, Y + l is a closed manifold with n^ = Gx *H G2, n> 4, there is a decomposition Y~YtUx Y2 with ir1(Yx) = G1,irl(Yl) = G2, itt(X) = H. For large classes of fundamental groups, the codimension one splitting theorems of [C3], extendi...

Three-manifolds with Fundamental Group a Free Product by William Jaco

Surgery on Closed 4-manifolds with Free Fundamental Group

The 4-dimensional topological surgery conjecture has been established for a class of groups, including the groups of subexponential growth (see [6], [13] for recent developments), however the general case remains open. The full surgery conjecture is known to be equivalent to the question for a class of canonical problems with free fundamental group [5, Chapter 12]. The proof of the conjecture f...

Surfaces in Three-manifolds with Hyperbolic Fundamental Group

We show that if a closed irreducible three-manifold with hyperbolic fundamental group contains a surface subgroup satisfying a certain geometric regularity assumption, then the surface is either quasiconvex or a virtual fiber. In the latter case, the manifold is hyperbolic. The regularity condition ensures that we may find algebraic bounds on the surface group which are analogous to the diamete...

Diffeomorphisms of Manifolds with Finite Fundamental Group

We show that the group 3i{M) of pseudoisotopy classes of diffeomorphisms of a manifold of dimension > 5 and of finite fundamental group is commensurable to an arithmetic group. As a result n0{DiffM) is a group of finite type. Let M be an «-dimensional closed smooth manifold, where n > 5, and let DiffM be the group of diffeomorphisms of M. The space DiffM (it is a topological space with the C°°-...