A mod 2 index theorem for \(\mathrm{pin}^-\) manifolds (Q1701249)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A mod 2 index theorem for \(\mathrm{pin}^-\) manifolds |
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A mod 2 index theorem for \(\mathrm{pin}^-\) manifolds (English)
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22 February 2018
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In this nice paper, the author establishes a \(\bmod\, 2\) index theorem for real vector bundles over \((8k+2)\)-dimensional compact \(\mathrm{pin}^-\) manifolds. The analytic index is the reduced \(\eta\) invariant of (twisted) Dirac operators and the topological index is defined through KO-theory. The main result extends the \(\bmod\,2\) index theorem of \textit{M. F. Atiyah} and \textit{I. M. Singer} [Ann. Math. (2) 93, 119--138, 139--149 (1971; Zbl 0212.28603)] to non-orientable manifolds.
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pin manifolds
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mod 2 index
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\(\eta\)-invariant
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