The odd spectral localiser via asymptotic morphisms and quasi-projections
K-Theory and Homology
2026-04-01 v2 Operator Algebras
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.
Keywords
Cite
@article{arxiv.2506.17143,
title = {The odd spectral localiser via asymptotic morphisms and quasi-projections},
author = {Yuezhao Li and Bram Mesland},
journal= {arXiv preprint arXiv:2506.17143},
year = {2026}
}
Comments
References and acknowledgement updated. A few typos fixed. 42 pages, 1 figure