The geometry of determinant line bundles in noncommutative geometry

DOI10.4171/JNCG/46zbMath1181.58020arXiv0804.3232MaRDI QIDQ734816

Varghese Mathai, Partha Sarathi Chakraborty

Publication date: 14 October 2009

Published in: Journal of Noncommutative Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0804.3232

zbMATH Keywords

regularitygauge transformationdimension spectrumconnectionindex theoremspectral tripledeterminant line bundle

Mathematics Subject Classification ID

Noncommutative differential geometry (46L87) Index theory and related fixed-point theorems on manifolds (58J20) Determinants and determinant bundles, analytic torsion (58J52) Noncommutative geometry (à la Connes) (58B34) Noncommutative global analysis, noncommutative residues (58J42)

Related Items (3)

The bordism group of unbounded KK-cycles ⋮ Curvature of the determinant line bundle for the noncommutative two torus ⋮ A reconstruction theorem for almost-commutative spectral triples

Cites Work

• Inner fluctuations of the spectral action
• Determinants of Cauchy-Riemann operators on a Riemann surface
• Supersymmetric quantum theory and non-commutative geometry
• Eigenvalue inequalities and Poincaré duality in noncommutative geometry
• BRS cohomology and the Chern character in noncommutative geometry
• The local index formula in noncommutative geometry
• Analytic torsion for complex manifolds
• Dirac operators coupled to vector potentials
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