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arXiv · 2506.17143

The odd spectral localiser via asymptotic morphisms and quasi-projections

Yuezhao Li·Bram Mesland
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Abstract

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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Yuezhao Li, Bram Mesland. 2025-06-20. The odd spectral localiser via asymptotic morphisms and quasi-projections. https://doi.org/10.2140/akt.2026.11.213

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