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 Spin^c 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.