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

2024/09/19 by Gennadi Kasparov, Kasparov, Gennadi
Mathematics · #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2409.19002

openalex publication_date 2024/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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