D-Bar Operators on Quantum Domains
Slawomir Klimek, Matthew McBride
TL;DR
This paper investigates the index problem for d-bar operators with Atiyah-Patodi-Singer boundary conditions on noncommutative geometric spaces like disks and annuli, advancing understanding in noncommutative analysis.
Contribution
It introduces the analysis of d-bar operators with APS boundary conditions in noncommutative domains, a novel extension of classical index theory.
Findings
Computed the index for d-bar operators on noncommutative disks and annuli.
Extended classical index theory to noncommutative geometric settings.
Provided new insights into boundary value problems in noncommutative geometry.
Abstract
We study the index problem for the d-bar operators subject to Atiyah- Patodi-Singer boundary conditions on noncommutative disk and annulus.
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