摘要
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.
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.
