The index of projective families of elliptic operators: the decomposable case
The index of projective families of elliptic operators: the decomposable case
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椭圆算子射影族的索引：可分解情况
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
I. Singer
中科院分区：
文献类型：
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作者：
V. Mathai;R. Melrose;I. Singer
当扭曲类（即 Dixmier-Douady）可分解时，发展了椭圆伪微分算子射影族的指数理论。这种特殊情况的特征之一是相应的 Azumaya 束可以用平滑算子来实现。椭圆算子射影族的拓扑索引和解析索引均取参数化空间的扭曲 K 理论中的值。主要结果是这两个索引概念的相等性。然后通过 Chern-Weil 理论的变体来计算索引类的扭曲 Chern 特征。
An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable. One of the features of this special case is that the corresponding Azumaya bundle can be realized in terms of smoothing operators. The topological and the analytic index of a projective family of elliptic operators both take values in the twisted K-theory of the parameterizing space. The main result is the equality of these two notions of index. The twisted Chern character of the index class is then computed by a variant of Chern-Weil theory.