8. Miscellaneous Problems

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 nonnegative sectional curvature, available at http://aimpl.org/nnsectcurvature.