The odd spectral localiser via asymptotic morphisms and quasi-projections
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866917373852778496 |
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| author | Li, Yuezhao Mesland, Bram |
| author_facet | Li, Yuezhao Mesland, Bram |
| contents | We describe the index pairing between an odd K-theory class and an odd unbounded Kasparov module by a pair of quasi-projections, supported on a submodule obtained from a finite spectral truncation. We achieve this by pairing the K-theory class with an asymptotic morphism determined by the unbounded Kasparov module. We interpret the spectral localiser of Loring and Schulz-Baldes as an instance of such an index pairing. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_17143 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The odd spectral localiser via asymptotic morphisms and quasi-projections Li, Yuezhao Mesland, Bram K-Theory and Homology Operator Algebras 19K35, 46L80 We describe the index pairing between an odd K-theory class and an odd unbounded Kasparov module by a pair of quasi-projections, supported on a submodule obtained from a finite spectral truncation. We achieve this by pairing the K-theory class with an asymptotic morphism determined by the unbounded Kasparov module. We interpret the spectral localiser of Loring and Schulz-Baldes as an instance of such an index pairing. |
| title | The odd spectral localiser via asymptotic morphisms and quasi-projections |
| topic | K-Theory and Homology Operator Algebras 19K35, 46L80 |
| url | https://arxiv.org/abs/2506.17143 |