Relative K-homology of higher-order differential operators
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866917683878952960 |
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| author | Fries, Magnus |
| author_facet | Fries, Magnus |
| contents | We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order relative spectral triple gives rise to a relative K-homology cycle. In the case of an elliptic differential operator on a compact smooth manifold with boundary, we calculate the K-homology boundary map of the constructed relative K-homology cycle to obtain a generalization of the Baum-Douglas-Taylor index theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_01977 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Relative K-homology of higher-order differential operators Fries, Magnus K-Theory and Homology Analysis of PDEs Functional Analysis Operator Algebras We extend the notion of a spectral triple to that of a higher-order relative spectral triple, which accommodates several types of hypoelliptic differential operators on manifolds with boundary. The bounded transform of a higher-order relative spectral triple gives rise to a relative K-homology cycle. In the case of an elliptic differential operator on a compact smooth manifold with boundary, we calculate the K-homology boundary map of the constructed relative K-homology cycle to obtain a generalization of the Baum-Douglas-Taylor index theorem. |
| title | Relative K-homology of higher-order differential operators |
| topic | K-Theory and Homology Analysis of PDEs Functional Analysis Operator Algebras |
| url | https://arxiv.org/abs/2308.01977 |