Spectral Sections and Higher Atiyah-Patodi-Singer Index Theory on Galois Coverings

被引：0
|
作者：
E. Leichtnam
P. Piazza
机构：
[1] Eric Leichtnam,
[2] École Normale Supérieure,undefined
[3] DMI,undefined
[4] 45 rue d'Ulm,undefined
[5] F-75230 Paris,undefined
[6] France,undefined
[7] e-mail: Eric.Leichtnam@ens.fr ,undefined
[8] Paolo Piazza,undefined
[9] Università di Roma "La Sapienza",undefined
[10] Istituto "G. Castelnuovo",undefined
[11] P. le A. Moro 2,undefined
[12] I-00185 Roma,undefined
[13] Italy,undefined
[14] e-mail: piazza@mat.uniroma1.it,undefined
来源：
Geometric & Functional Analysis GAFA | 1998年 / 8卷
关键词：
Boundary Operator; Dirac Operator; High Index; Polynomial Growth; Index Theorem;
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学科分类号：
摘要：
In this paper we consider \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \Gamma \to \tilde M \to M $\end{document} a Galois covering with boundary and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \not \tilde D $\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \Gamma $\end{document}-invariant generalized Dirac operator on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \tilde M $\end{document}. We assume that the group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \Gamma $\end{document} is of polynomial growth with respect to a word metric. By employing the notion of noncommutative spectral section associated to the boundary operator \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \not \tilde D_0 $\end{document} and the b-calculus on Galois coverings with boundary, we develop a higher Atiyah-Patodi-Singer index theory. Our main theorem extends to such \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $ \Gamma $\end{document}-Galois coverings with boundary the higher index theorem of Connes-Moscovici.
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页码：17 / 58
页数：41
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