The odd spectral localiser via asymptotic morphisms and quasi-projections
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.
Fields of Study & Subjects
Advanced Operator Algebra Research
Algebraic structures and combinatorial models
Holomorphic and Operator Theory
Publication details
- Journal / source
- Annals of K-Theory
- Volume
- 11
- Issue
- 2
- Pages
- 213–260
- Publication date
- 30 March 2026
- Language
- EN