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

Fuente: arXiv
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Auteur principal: Kasparov, Gennadi
Format: Preprint
Publié: 2024
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author Kasparov, Gennadi
author_facet Kasparov, Gennadi
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2409_19002
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Coarse pseudo-differential calculus and index theory on manifolds with a tangent Lie structure
Kasparov, Gennadi
Differential Geometry
Functional Analysis
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.
title Coarse pseudo-differential calculus and index theory on manifolds with a tangent Lie structure
topic Differential Geometry
Functional Analysis
url https://arxiv.org/abs/2409.19002