The eta invariant and equivariant bordism of flat manifolds with cyclic holonomy group of odd prime order

被引：0
作者：
Peter B. Gilkey
Roberto J. Miatello
Ricardo A. Podestá
机构：
[1] University of Oregon,Mathematics Department
[2] FaMAF – CIEM,undefined
[3] Universidad Nacional de Córdoba,undefined
来源：
Annals of Global Analysis and Geometry | 2010年 / 37卷
关键词：
Flat manifolds; Eta invariant; Equivariant bordism; 58J53;
D O I：
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学科分类号：
摘要：
We study the eta invariants of compact flat spin manifolds of dimension n with holonomy group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{Z}_p}$$\end{document}, where p is an odd prime. We find explicit expressions for the twisted and relative eta invariants and show that the reduced eta invariant is always an integer, except in a single case, when p = n = 3. We use the expressions obtained to show that any such manifold is trivial in the appropriate reduced equivariant spin bordism group.
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页码：275 / 306
页数：31
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