Manifolds with non-stable fundamental groups at infinity.
We prove that the mass endomorphism associated to the Dirac operator on a Riemannian manifold is non-zero for generic Riemannian metrics. The proof involves a study of the mass endomorphism under surgery, its behavior near metrics with harmonic spinors, and analytic perturbation arguments.
We study self-homotopy equivalences and diffeomorphisms of the (n+1)-dimensional manifold X= #p(S1 x Sn) for any n ≥ 3. Then we completely determine the group of pseudo-isotopy classes of homeomorphisms of X and extend to dimension n well-known theorems due to F. Laudenbach and V. Poenaru (1972,1973), and J. M. Montesinos (1979).
Given a closed 4-manifold M, let M* be the simply-connected 4-manifold obtained from M by killing the fundamental group. We study the relation between the intersection forms λM and λM*. Finally some topological consequences and examples are described.