
## 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.