Spectral geometry, Riemannian submersions, and the Gromov-Lawson conjecture Book

ELLIPTIC OPERATORS Introduction The Real and Complex Laplace Operators Spinors Spectral Resolutions Manifolds with Boundary Spectral Invariants The Eta Invariant Computing the Eta Invariant DIFFERENTIAL GEOMETRY Introduction Riemannian Submersions Characteristic Classes The Geometry of Sphere and Principal Bundles The Geometry of Circle Bundles The Hopf Fibration The Scalar Curvature Levi-Civita and Spin Connections POSITIVE CURVATURE Introduction Manifolds with Positive Ricci Curvature Bordism and Connective K Theory Calculations Involving the Eta Invariant The Eta Invariant and Connective K Theory Computing Connective K Theory Groups SPECTRAL GEOMETRY OF RIEMANNIAN SUBMERSIONS Introduction Intertwining the Coderivitives The Real Laplacian The Complex Laplacian The Spin Laplacian Riemannian Submersions with Boundary Heat Trace and Heat Content Unresolved Questions REFERENCES Introduction Main Bibliography Bibliography of Harmonic Morphisms Parabolic PDE Bibliography NOTATION INDEX