Botvinnik, BorisGranath, Elliot2024-01-102024-01-102024-01-10https://hdl.handle.net/1794/29212In 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-USAll Rights Reserved.bordismbundlecobordismspintopologytransferElectronic Thesis or Dissertation