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arXiv · 2007.06239

A lattice version of the Atiyah-Singer index theorem

Mayuko Yamashita
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Abstract

We formulate and prove a lattice version of the Atiyah-Singer index theorem. The main theorem gives a $K$-theoretic formula for an index-type invariant of operators on lattice approximations of closed integral affine manifolds. We apply the main theorem to an index problem of Wilson-Dirac operators in lattice gauge theory.

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BibTeXRIS

Mayuko Yamashita. 2020-07-13. A lattice version of the Atiyah-Singer index theorem. https://doi.org/10.1007/s00220-021-04021-1

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