Moduli spaces of Ricci positive metrics in dimension five
McFeely Jackson Goodman

TL;DR
This paper uses eta invariants of spin^c Dirac operators to distinguish connected components in the moduli spaces of Ricci positive metrics on five-dimensional manifolds, revealing infinitely many components for certain manifolds.
Contribution
It introduces a method to distinguish moduli space components using eta invariants and constructs infinitely many non-diffeomorphic 5-manifolds with complex moduli space structures.
Findings
Identified infinitely many components in moduli spaces of Ricci positive metrics.
Classified 5-manifolds with fundamental group Z_2 admitting free S^1 actions.
Constructed examples of manifolds with complex moduli space topology.
Abstract
We use the invariants of spin 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 bundles over and the metrics are lifted from Ricci positive metrics on the bases. Along the way we classify 5-manifolds with fundamental group admitting free actions with simply connected quotients.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric Analysis and Curvature Flows · Advanced Differential Geometry Research · Geometry and complex manifolds
