Mcfeely Jackson Goodman, UC Berkeley

Title: Moduli spaces of Ricci positive metrics in dimension five.

Abstract: Invariants related to the spectra of Dirac operators
can be used to determine when two Riemannian metrics cannot be
connected with a path of metrics maintaining a certain curvature
condition. We use the eta invariant of Spinc Dirac operators to
distinguish connected components of moduli spaces of Riemannian
metrics with positive Ricci curvature. We then find infinitely many
non-diffeomorphic five dimensional manifolds for which these moduli
spaces each have infinitely many components. The manifolds are total
spaces of principal S1 bundles over connected sums of complex
projective space and the metrics are lifted from Ricci positive
metrics on the base.