FMSP Lectures

Seminar information archive ~03/27Next seminarFuture seminars 03/28~


2018/10/24

15:00-16:30   Room #123 (Graduate School of Math. Sci. Bldg.)
Paul Baum (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (2/4)
Lecture 2. THE DIRAC OPERATOR (ENGLISH)
[ Abstract ]
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.
[ Reference URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf