Coarse pseudo-differential calculus and index theory on manifolds with a tangent Lie structure

Gennadi Kasparov

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arXiv · 2409.19002

Coarse pseudo-differential calculus and index theory on manifolds with a tangent Lie structure

Gennadi Kasparov

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Abstract

We introduce a simplified (coarse) version of pseudo-differential calculus for operators of order zero on complete Riemannian manifolds. This calculus works for the usual Hormander (1,0) class of operators, as well as for pseudo-differential operators on filtered manifolds. In fact, we develop the coarse PDO calculus on a more general class of manifolds which we call manifolds with a tangent Lie structure. We prove an index theorem for `h-elliptic' operators where the index is not just an integer, but an element of the K-homology group of the manifold.

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Gennadi Kasparov. 2024-09-19. Coarse pseudo-differential calculus and index theory on manifolds with a tangent Lie structure. https://arxiv.org/abs/2409.19002

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