D-bar operators on quantum domains

DOI10.1007/s11040-010-9084-9zbMath1252.46072arXiv1001.2216OpenAlexW1994629586MaRDI QIDQ430029

Matt McBride, Sławomir Klimek-Chudy

Publication date: 20 June 2012

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.2216

zbMATH Keywords

noncommutative geometryDirac operatorFredholm operatorindexparametrixquantum spaceAPS boundary conditionsd-bar operatorquantum annulusquantum disk

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Index theory and related fixed-point theorems on manifolds (58J20) Geometry of quantum groups (58B32)

Related Items

Derivations and reflection positivity on the quantum cylinder ⋮ A p-adic spectral triple ⋮ Derivations and spectral triples on quantum domains. I: Quantum disk ⋮ Derivations and spectral triples on quantum domains II: quantum annulus ⋮ A Dirac type operator on the non-commutative disk ⋮ Dirac type operators on the quantum solid torus with global boundary conditions ⋮ A note on spectral triples on the quantum disk ⋮ Classical limit of the d-bar operators on quantum domains ⋮ Global boundary conditions for a Dirac operator on the solid torus

Cites Work

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• Quantum Riemann surfaces. I: The unit disc
• Quantum Riemann surfaces. III: The exceptional cases
• Supersymmetry and Fredholm modules over quantized spaces
• Noncommutative complex analysis and Bargmann-Segal multipliers
• Noncommutative Atiyah-Patodi-Singer boundary conditions and index pairings in KK-theory
• Spectral asymmetry and Riemannian Geometry. I
• Connes–Chern character for manifolds with boundary and eta cochains

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