Geography of pinched four-manifolds

Abstract

We prove several new restrictions on the Euler characteristic and signature of oriented 4-manifolds with (positively or negatively) pinched sectional curvature. In particular, we show that simply connected 4-manifolds with $\hat{I}´\le \sec \le 1$, where $\hat{I}´=\frac{1}{1+3\sqrt{3}}\cong 0.161$, are homeomorphic to $S^4$ or $\mathbb{C}{P}^2$.

LaTeX2e, 37 pages, 2 figures, final version