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Rademacher Lectures

Tuesday, April 10, 2018 - 3:30pm

Paul Baum

Pennsylvania State University

Location

University of Pennsylvania

A4 DRL

Tea will be served at 3:00pm in 4E17 DRL

Lecture 2. THE DIRAC OPERATOR

The Dirac operator of R^n will be defined. This is a first order elliptic differential operator with constant coefficients.
Next, the class of differentiable manifolds which come equipped with an order one differential operator which (at the symbol level) is locally isomorphic to the Dirac operator of R^n will be considered. These are the Spin-c manifolds.
Spin-c is slightly stronger than oriented, so Spin-c can be viewed as "oriented plus epsilon". Most of the oriented manifolds that occur in practice are Spin-c. The Dirac operator of a closed Spin-c manifold is the basic example for the Hirzebruch-Riemann-Roch theorem and the Atiyah-Singer index theorem.