A Positively Curved Manifold Homeomorphic
نویسنده
چکیده
Spaces of positive curvature play a special role in geometry. Although the class of manifolds with positive (sectional) curvature is expected to be relatively small, so far there are only a few known obstructions. Moreover, for closed simply connected manifolds these coincide with the known obstructions to nonnegative curvature which are: (1) the Betti number theorem of Gromov which asserts that the homology of a compact manifold with non-negative sectional curvature has an a priori bound on the number of generators depending only on the dimension, and (2) a result of Lichnerowicz and Hitchin implying that a spin manifold with non-trivial  genus or generalized a genus cannot admit a metric with non negative curvature.
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