Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics
| dc.contributor.advisor | Stern, Mark A | |
| dc.contributor.author | Andreae, Phillip | |
| dc.date.accessioned | 2016-09-29T14:40:03Z | |
| dc.date.available | 2016-09-29T14:40:03Z | |
| dc.date.issued | 2016 | |
| dc.department | Mathematics | |
| dc.description.abstract | The central idea of this dissertation is to interpret certain invariants constructed from Laplace spectral data on a compact Riemannian manifold as regularized integrals of closed differential forms on the space of Riemannian metrics, or more generally on a space of metrics on a vector bundle. We apply this idea to both the Ray-Singer analytic torsion and the eta invariant, explaining their dependence on the metric used to define them with a Stokes' theorem argument. We also introduce analytic multi-torsion, a generalization of analytic torsion, in the context of certain manifolds with local product structure; we prove that it is metric independent in a suitable sense. | |
| dc.identifier.uri | ||
| dc.subject | Mathematics | |
| dc.subject | Analysis | |
| dc.subject | analytic torsion | |
| dc.subject | eta invariant | |
| dc.subject | Geometry | |
| dc.subject | Topology | |
| dc.title | Analytic Torsion, the Eta Invariant, and Closed Differential Forms on Spaces of Metrics | |
| dc.type | Dissertation |
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