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The spectral localizer for semifinite spectral triples


Authors: Hermann Schulz-Baldes and Tom Stoiber
Journal: Proc. Amer. Math. Soc. 149 (2021), 121-134
MSC (2010): Primary 19K56, 46L80
DOI: https://doi.org/10.1090/proc/15230
Published electronically: October 20, 2020
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Abstract: The notion of a spectral localizer is extended to pairings with semifinite spectral triples. By a spectral flow argument, any semifinite index pairing is shown to be equal to the signature of the spectral localizer. As an application, a formula for the weak invariants of topological insulators is derived. This provides a new approach to their numerical evaluation.


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Additional Information

Hermann Schulz-Baldes
Affiliation: Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

Tom Stoiber
Affiliation: Department Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, Germany

DOI: https://doi.org/10.1090/proc/15230
Received by editor(s): February 11, 2020
Received by editor(s) in revised form: May 27, 2020, and June 8, 2020
Published electronically: October 20, 2020
Communicated by: Adrian Ioana
Article copyright: © Copyright 2020 American Mathematical Society