## FMSPレクチャーズ

担当者 河野俊丈

### 2018年10月24日(水)

15:00-16:30   数理科学研究科棟(駒場) 123号室
Paul Baum 氏 (The Pennsylvania State University)
K-THEORY AND THE DIRAC OPERATOR (2/4)
Lecture 2. THE DIRAC OPERATOR (ENGLISH)
[ 講演概要 ]
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.
[ 講演参考URL ]
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Baum.pdf