Coronas and Callias type operators in coarse geometry
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866913572543528960 |
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| author | Bunke, Ulrich Ludewig, Matthias |
| author_facet | Bunke, Ulrich Ludewig, Matthias |
| contents | We interpret the coarse symbol and index class of a Callias type Dirac operator $D+Ψ$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$ itself determined by $Ψ$. Local positivity of $D$ and local invertibility of $Ψ$ are incorporated in terms of support conditions on the $K$-theoretic level. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_01646 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Coronas and Callias type operators in coarse geometry Bunke, Ulrich Ludewig, Matthias K-Theory and Homology Algebraic Topology Differential Geometry Operator Algebras We interpret the coarse symbol and index class of a Callias type Dirac operator $D+Ψ$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$ itself determined by $Ψ$. Local positivity of $D$ and local invertibility of $Ψ$ are incorporated in terms of support conditions on the $K$-theoretic level. |
| title | Coronas and Callias type operators in coarse geometry |
| topic | K-Theory and Homology Algebraic Topology Differential Geometry Operator Algebras |
| url | https://arxiv.org/abs/2411.01646 |