arXiv:2007.06239·v3·math.DG
A lattice version of the Atiyah-Singer index theorem
Abstract
We formulate and prove a lattice version of the Atiyah-Singer index theorem. The main theorem gives a -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.
Comments: 27 pages, final version