标题： 微分算子的同调 I. 有边界的流形 显示英文标题

标题： Homology of pseudodifferential operators I. Manifolds with boundary

摘要： Hochschild同调群和循环同调群对于任何有边界的紧流形上的尖点伪微分算子代数进行了计算。该代数的指标泛函被解释为Hochschild 1-上循环，并通过两个自然理想的迹函数的扩展来评估，这两个理想分别对应于内部阶数和边界处消失次数的两个滤过结构，同时还包括代数的外导数。这导致了一个指标公式，这是Atiyah、Patodi和Singer为Dirac算子提出的公式的伪微分扩展；它与一个符号项一起涉及由第一位作者之前在边界上的悬浮代数中引入的“eta”不变量。 显示英文摘要

摘要： The Hochschild and cyclic homology groups are computed for the algebra of `cusp' pseudodifferential operators on any compact manifold with boundary. The index functional for this algebra is interpreted as a Hochschild 1-cocycle and evaluated in terms of extensions of the trace functionals on the two natural ideals, corresponding to the two filtrations by interior order and vanishing degree at the boundary, together with the exterior derivations of the algebra. This leads to an index formula which is a pseudodifferential extension of that of Atiyah, Patodi and Singer for Dirac operators; together with a symbolic term it involves the `eta' invariant on the suspended algebra over the boundary previously introduced by the first author.