Geometry/topology Seminar
Monday, March 15, 2021, 3:15pm, Zoom link
Mcfeely Jackson Goodman (Berkeley, Mathematics)
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 S^1 bundles over connected sums of complex projective space and the metrics are lifted from Ricci positive metrics on the base.

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