Tate tame symbol and the joint torsion of commuting operators

Jens Kaad, Ryszard Nest

Research output: Contribution to journalJournal articleResearchpeer-review

9 Downloads (Pure)

Abstract

We investigate determinants of Koszul complexes of holomorphic functions of a commuting tuple of bounded operators acting on a Hilbert space. Our main result shows that the analytic joint torsion, which compares two such determinants, can be computed by a local formula which involves a tame symbol of the involved holomorphic functions. As an application we are able to extend the classical tame symbol of meromorphic functions on a Riemann surface to the more involved setting of transversal functions on a complex analytic curve. This follows by spelling out our main result in the case of Toeplitz operators acting on the Hardy space over the polydisc.
Original languageEnglish
JournalAnnals of K-Theory
Volume5
Issue number2
Pages (from-to)181-211
ISSN2379-1683
DOIs
Publication statusPublished - 20. Jun 2020

Fingerprint Dive into the research topics of 'Tate tame symbol and the joint torsion of commuting operators'. Together they form a unique fingerprint.

Cite this