Manifolds with fundamental group a generalized free product. I

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...

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°°-...

The Fundamental Group of S1-manifolds

We address the problem of computing the fundamental group of a symplectic S-manifold for non-Hamiltonian actions on compact manifolds, and for Hamiltonian actions on non-compact manifolds with a proper moment map. We generalize known results for compact manifolds equipped with a Hamiltonian S-action. Several examples are presented to illustrate our main results.