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The odd spectral
localiser via asymptotic morphisms and quasi-projections
Yuezhao Li and Bram Mesland |
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Vol. 11 (2026), No. 2, 213–260
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Abstract |
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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. |
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Keywords
Kasparov theory, asymptotic morphisms, computational
$K$-theory
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Mathematical Subject Classification
Primary: 19K35, 46L80
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Milestones
Received: 15 July 2025
Revised: 28 October 2025
Accepted: 28 November 2025
Published: 30 March 2026
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Authors |
| Yuezhao Li | |
| Mathematisch Instituut Universiteit Leiden Leiden Netherlands |
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| Bram Mesland | |
| Mathematisch Instituut Universiteit Leiden Leiden Netherlands |
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| © 2026 MSP (Mathematical Sciences Publishers). |
