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 in lattice gauge theory.
A general collapsing result for families of stratified Riemannian metrics on orbifolds
Computer-assisted proof of the main theorem of 'The Classification of branched Willmore spheres in the $3$-sphere and the $4$-sphere'
A sufficient condition for a pair of bi-Lipschitz homeomorphic manifolds to be diffeomorphic and the diameter sphere theorem
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