Almost nonnegative curvature operator and cohomology rings |
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Authors: | Martin Herrmann |
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Institution: | 1. Fakultät für Mathematik, Karlsruher Institut für Technologie, Kaiserstraβe 89–93, 76133 Karlsruhe, Germany2. Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, 48149 Münster, Germany |
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Abstract: | We give a survey of results on the construction of and obstructions to metrics of almost nonnegative curvature operator on closed manifolds and results on the cohomology rings of closed, simply-connected manifolds with a lower curvature and upper diameter bound. The latter is motivated by a question of Grove whether these condition imply finiteness of rational homotopy types. This question has answers by F. Fang–X. Rong, B. Totaro and recently A. Dessai and the present author. |
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Keywords: | Nonnegative curvature homogeneous spaces curvature operator almost nonnegative curvature |
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