扭化的Atiyah-Singer算子(Ⅰ)(英文)

On Twisted Atiyah-Singer Operators(Ⅰ)

英文关键词:Clifford module  Spin group  elliptic operator  twisted Atiyah-Singer operator  index theorem

中文摘要:

      本文证明黎曼流形上的deRham以及Signature算子都同构于扭化的Atiyah－Singer算子.这两类算子的局部指数定理和局部Lefschetz不动点公式都可以从扭化的Atiyah-Singer算子得到．

英文摘要:

      In this paper we show that the de Rham and the Signature operators on a Riemannian manifold are all isomorphic to some twisted Atiyah-Singer operators. Then the local index theorem and local Lefschetz fixed point formulas of these operators can be obtained from the corresponding theorems of twisted Atiyah-Singer operators.