Index Theory for Invariant Elliptic Operators on Manifolds with Proper Cocompact Group Actions

Author

Gong Cheng, Washington University in St. LouisFollow

Date of Award

Summer 8-15-2018

Author's School

Graduate School of Arts and Sciences

Author's Department

Mathematics

Degree Name

Doctor of Philosophy (PhD)

Degree Type

Dissertation

Abstract

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.

Language

English (en)

Chair and Committee

Xiang Tang

Committee Members

Quo-Shin Chi, Renato Feres, Jr-Shin Li, Yanli Song,

Comments

Permanent URL: 2018-08-15

Recommended Citation

Cheng, Gong, "Index Theory for Invariant Elliptic Operators on Manifolds with Proper Cocompact Group Actions" (2018). Arts & Sciences Electronic Theses and Dissertations. 1616.
https://openscholarship.wustl.edu/art_sci_etds/1616