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8. Miscellaneous Problems


    1. Add remark

      Problem 8.1.

      Is a “generic” manifold a $K(\pi, 1)$-space (where “generic” is to be determined)?


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          Problem 8.2.

          Does positive sectional curvature imply that the manifold is formal (in the sense of Sullivan’s minimal model)?


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              Problem 8.3.

              For compact, odd dimensional, positively curved manifolds is there a cyclic subgroup of the fundamental group whose index is bounded only in terms of the dimension?


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                  Problem 8.4.

                  Is there a finiteness result for $n$-dimensional, positively curved manifolds with $\pi_1 = \pi_2 = 0$?


                    • Add remark

                      Problem 8.5.

                      Is there a $\delta(n) > 0$ such that any $n$-dimensional, positively curved manifold carries a $\delta(n)$-pinched metric?

                          Cite this as: AimPL: Manifolds with non-negative sectional curvature, available at http://aimpl.org/nnsectcurvature.