Coarse pseudo-differential calculus and index theory on manifolds with a tangent Lie structure
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915349374435328 |
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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 |