An index theorem for odd-dimensional \(\mathbb{Z}/k\mathbb{Z}\)-manifolds (Q2072019)
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scientific article; zbMATH DE number 7466921
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An index theorem for odd-dimensional \(\mathbb{Z}/k\mathbb{Z}\)-manifolds |
scientific article; zbMATH DE number 7466921 |
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An index theorem for odd-dimensional \(\mathbb{Z}/k\mathbb{Z}\)-manifolds (English)
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31 January 2022
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\textit{D. S. Freed} and \textit{R. B. Melrose} [Invent. Math. 107, No. 2, 283--299 (1992; Zbl 0760.58039)] gave a mod-\(k\) index theorem in even dimension, and in [J. Funct. Anal. 238, No. 1, 1--26 (2006; Zbl 1114.58011)] \textit{X. Dai} and \textit{W. Zhang} gave an index theorem for Toeplitz operators in odd dimension, for a manifold with boundary. The article under review proves a mod-\(k\) index theorem in odd dimension. The result bridges the results in [\textit{D. S. Freed} and \textit{R. B. Melrose}, Invent. Math. 107, No. 2, 283--299 (1992; Zbl 0760.58039)] and [\textit{X. Dai} and \textit{W. Zhang}, J. Funct. Anal. 238, No. 1, 1--26 (2006; Zbl 1114.58011)].
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\(\mathbb{Z}/K\mathbb{Z}\)-manifold
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spectral flow
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direct image
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geometric \(K\)-homology
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index theorems
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0.8370056748390198
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0.8333940505981445
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0.8332266211509705
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0.8252177238464355
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0.8129871487617493
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