无限维中的迹与特征类
Traces and Characteristic Classes in Infinite Dimensions
摘要：
本文综述了由非正阶伪微分算子代数上的两类迹所构造的特征类所得到的拓扑结果。主要结果是一个通用的$\hat A$ -多项式和陈特征的建设控制的$S^1$ -指标定理的一个固定的向量丛在流形上，和$|π_1({\rm Diff}(M^5))| = \infty$，为${\rm Diff}(M^5)$的圆丛$M^5$与大的第一陈类射影代数Kaehler曲面的同胚群。
英文摘要：
This paper surveys topological results obtained from characteristic classes built from the two types of traces on the algebra of pseudodifferential operators of nonpositive order. The main results are the construction of a universal $\hat A$-polynomial and Chern character that control the $S^1$-index theorem for all circle actions on a fixed vector bundle over a manifold, and $|π_1({\rm Diff}(M^5))| = \infty$, for ${\rm Diff}(M^5)$ the diffeomorphism group of circle bundles $M^5$ with large first Chern class over projective algebraic Kaehler surfaces.
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