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Date of Award
Doctor of Philosophy (PhD)
In this thesis, we study G-invariant elliptic operators, and in particular Dirac operators, on the space of invariant sections of a Hermitian bundle over a (non-compact) manifold with a proper and cocompact Lie group action. We provide a canonical way to define the Hilbert space of invariant sections for proper and cocompact actions and prove that the G-invariant Dirac operators, and more generally, elliptic operators, are Fredholm for the Hilbert space we constructed. Using the framework developed in this thesis, we give a new proof of a generalized Lichnerowicz Vanishing Theorem for proper cocompact group actions as an application.
Chair and Committee
Quo-Shin Chi, Renato Feres, Jr-Shin Li, Yanli Song,
Cheng, Gong, "Index Theory for Invariant Elliptic Operators on Manifolds with Proper Cocompact Group Actions" (2018). Arts & Sciences Electronic Theses and Dissertations. 1616.
Available for download on Monday, August 15, 2118