Scalar Curvature and Transfer Maps in Spin and Spin^c Bordism
| dc.contributor.advisor | Botvinnik, Boris | |
| dc.contributor.author | Granath, Elliot | |
| dc.date.accessioned | 2024-01-10T14:14:30Z | |
| dc.date.available | 2024-01-10T14:14:30Z | |
| dc.date.issued | 2024-01-10 | |
| dc.description.abstract | In 1992, Stolz proved that, among simply connected Spin-manifolds of dimension5 or greater, the vanishing of a particular invariant α is necessary and sufficient for the existence of a metric of positive scalar curvature. More precisely, there is a map α: ΩSpin → ko (which may be realized as the index of a Dirac operator) ∗ which Hitchin established vanishes on bordism classes containing a manifold with a metric of positive scalar curvature. Stolz showed kerα is the image of a transfer map ΩSpinBPSp(3) → ΩSpin. In this paper we prove an analogous result for Spinc- ∗−8 ∗ manifolds and a related invariant αc : ΩSpinc → ku. We show that ker αc is the ∗ sum of the image of Stolz’s transfer ΩSpinBPSp(3) → ΩSpinc and an analogous map ∗−8 ∗ ΩSpinc BSU(3) → ΩSpinc . Finally, we expand on some details in Stolz’s original paper ∗−4 ∗ and provide alternate proofs for some parts. | en_US |
| dc.identifier.uri | https://hdl.handle.net/1794/29212 | |
| dc.language.iso | en_US | |
| dc.publisher | University of Oregon | |
| dc.rights | All Rights Reserved. | |
| dc.subject | bordism | en_US |
| dc.subject | bundle | en_US |
| dc.subject | cobordism | en_US |
| dc.subject | spin | en_US |
| dc.subject | topology | en_US |
| dc.subject | transfer | en_US |
| dc.title | Scalar Curvature and Transfer Maps in Spin and Spin^c Bordism | |
| dc.type | Electronic Thesis or Dissertation | |
| thesis.degree.discipline | Department of Mathematics | |
| thesis.degree.grantor | University of Oregon | |
| thesis.degree.level | doctoral | |
| thesis.degree.name | Ph.D. |
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