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This study investigates the index homomorphism of even K-groups in KK-theory using spectral localizers.

Spectral localizers in $KK$-theory

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We study spectral localizers and index homomorphism in KK-theory, indicating new links with K-homology.

This study investigates the index homomorphism of even K-groups in KK-theory using spectral localizers.
Utilized the Kasparov product to examine even KK-theory and K-groups.
Developed an explicit formula for the index homomorphism based on spectral localizers related to the Dirac operator.
Applied continuous compactly supported functions to the Dirac operator in the context of Hilbert C*-modules.
Established that the index homomorphism can be solely described using a compact interval intersecting with the spectrum of the Dirac operator.
Showed the formulation connects the K-theoretic components and the characteristics of the Dirac operator.
Recovered previous results on index pairing under the condition of even KK-theory coinciding with even K-homology.

Jens Kaad (2026) studied this question.

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