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arXiv · 2106.02138

Geography of pinched four-manifolds

Renato G. Bettiol·Mario Kummer·Ricardo A. E. Mendes
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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 $\delta\leq \sec\leq 1$, where $\delta=\frac{1}{1+3\sqrt3}\cong 0.161$, are homeomorphic to $S^4$ or $\mathbb C P^2$.

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Renato G. Bettiol, Mario Kummer, Ricardo A. E. Mendes. 2021-06-03. Geography of pinched four-manifolds. https://doi.org/10.4310/cag.241120233719

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