MODULI SPACE OF METRICS OF NONNEGATIVE SECTIONAL OR POSITIVE RICCI CURVATURE ON HOMOTOPY REAL PROJECTIVE SPACES

We show that the moduli space of metrics of nonnegative sectional curvature on every homotopy RP5 has infinitely many path components. We also show that in each dimension 4k + 1 there are at least 2(2k) homotopy RP4k+1's of pairwise distinct oriented diffeomorphism type for which the moduli space of metrics of positive Ricci curvature has infinitely many path components. Examples of closed manifolds with finite fundamental group with these properties were known before only in dimensions 4k + 3 >= 7.

Automated summary

In our study, we found that the moduli space of metrics on certain homotopy spaces can have multiple path components with distinct properties. The existence of such examples was previously known only in higher dimensions.