| Register
\(\newcommand{\Cat}{{\rm Cat}} \) \(\newcommand{\A}{\mathcal A} \) \(\newcommand{\freestar}{ \framebox[7pt]{$\star$} }\)

8. Miscellaneous Problems

    1. Problem 8.1.

      Is a “generic” manifold a $K(\pi, 1)$-space (where “generic” is to be determined)?
        • Problem 8.2.

          Does positive sectional curvature imply that the manifold is formal (in the sense of Sullivan’s minimal model)?
            • 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?
                • Problem 8.4.

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