Doing surgery on the 5-torus, we construct a 5-dimensional closed spin-manifold M with π1(M) ∼= Z ×Z/3, so that the index invariant in the KO-theory of the reduced C-algebra of π1(M) is zero. Then we use the theory of minimal surfaces of Schoen/Yau to show that this manifolds cannot carry a metric of positive scalar curvature. The existence of such a metric is predicted by the (unstable) Gromov...

In this paper, the δ-hyperbolic concept, originally developed for infinite graphs, is adapted to very large but finite graphs. Such graphs can indeed exhibit properties typical of negatively curved spaces, yet the traditional δ-hyperbolic concept, which requires existence of an upper bound on the fatness δ of the geodesic triangles, is unable to capture those properties, as any finite graph has...

On a compact Kähler manifold X with a holomorphic 2-form α, there is an almost complex structure associated with α. We show how this implies vanishing theorems for the Gromov-Witten invariants ofX . This extends the approach, used in [LP] for Kähler surfaces, to higher dimensions. Let X be a Kähler surface with a non-zero holomorphic 2-form α. Then α is a section of the canonical bundle and its...