论文标题
在佩罗的索引共生
On Perrot's index cocycles
论文作者
论文摘要
由于Denis Perrot，我们将提出一个简化的构造版本，该版本从JLO型循环循环中恢复了复杂的切线束的TODD类。该结构发生在代数框架内，而不是JLO理论的习惯功能分析框架。指数函数的串联扩展由功能分析理论代替热内核。选择的狄拉克操作员远非椭圆形； Perrot发现的一个了不起的新迹线取代了操作员跟踪。佩罗特（Perrot）的理论完整形式构成了一种全新的索引理论方法。此处介绍的帐户涵盖了大多数但并非全部。
We shall present a simplified version of a construction due to Denis Perrot that recovers the Todd class of the complexified tangent bundle from a JLO-type cyclic cocycle. The construction takes place within an algebraic framework, rather than the customary functional-analytic framework for the JLO theory. The series expansion for the exponential function is used in place of the heat kernel from the functional-analytic theory; the Dirac operator chosen is far from elliptic; and a remarkable new trace discovered by Perrot replaces the operator trace. In its full form Perrot's theory constitutes a wholly new approach to index theory. The account presented here covers most but not all of this approach.
