### Geometry-Topology Seminar

Tuesday, November 19, 2019 - 4:30pm

#### Jackson Goodman

UPenn

Location

University of Pennsylvania

DRL 4N30

The Geometry-Topology Seminar will not meet this Thursday November 21.

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 manifolds $$(#^k S^2 \times S^3)/\mathbb{Z}_2$$ for which these moduli spaces each have infinitely many components.  The manifolds are total spaces of principal $$S^1$$ bundles and the metrics are lifted from Ricci positive metrics on the bases using a method of Gilkey, Park, and Tuschmann.  We compute the eta invariants by extending metrics and auxiliary connections over the associated disc bundles, generalizing a technique of Kreck and Stolz.