Index Theory and Non-Commutative Geometry II. Dirac Operators and Index Bundles

被引：15

作者：

Benameur, Moulay-Tahar ^{[1
]}

Heitsch, James L. ^{[2
,3
]}

机构：

[1] Univ Metz, CNRS, UMR 7122, Metz, France

[2] Univ Illinois, Chicago, IL USA

[3] Northwestern Univ, Evanston, IL 60208 USA

来源：

JOURNAL OF K-THEORY | 2008年 / 1卷 / 02期

关键词：

Non-commutative geometry; foliation; index theory; Dirac operator; index bundle;

D O I：

10.1017/is007011012jkt007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

When the index bundle of a longitudinal Dirac type operator is transversely smooth, we define its Chem character in Haefliger cohomology and relate it to the Chem character of the K-theory index. This result gives a concrete connection between the topology of the foliation and the longitudinal index formula. Moreover, the usual spectral assumption on the Novikov-Shubin invariants of the operator is improved.

引用

页码：305 / 356

页数：52

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