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arXiv · 1508.02619

A mod 2 index theorem for pin$^-$ manifolds

Weiping Zhang
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Abstract

We establish a mod 2 index theorem for real vector bundles over 8k+2 dimensional compact pin$^-$ manifolds. The analytic index is the reduced $\eta$ invariant of (twisted) Dirac operators and the topological index is defined through $KO$-theory. Our main result extends the mod 2 index theorem of Atiyan and Singer to non-orientable manifolds.

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Weiping Zhang. 2015-08-11. A mod 2 index theorem for pin$^-$ manifolds. https://arxiv.org/abs/1508.02619

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