Splitting the curvature of the determinant line bundle

DOI10.1090/S0002-9939-99-05311-3zbMath0957.58025arXivmath/9812124WikidataQ125878726 ScholiaQ125878726MaRDI QIDQ4490240

Simon G. Scott

Publication date: 10 July 2000

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/9812124

zbMATH Keywords

Quillen metricdeterminant bundleanalytic surgeryBismut-Freed connectionGrassmann section

Mathematics Subject Classification ID

Anomalies in quantum field theory (81T50) Boundary value problems on manifolds (58J32) Determinants and determinant bundles, analytic torsion (58J52)

Related Items (5)

Zeta determinants on manifolds with boundary ⋮ On the relationship of gerbes to the odd families index theorem ⋮ Relative zeta determinants and the geometry of the determinant line bundle ⋮ Boundary currents and Hamiltonian quantization of fermions in background fields ⋮ Determinant bundles, boundaries, and surgery

Cites Work

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• The Atiyah-Singer index theorem for families of Dirac operators: Two heat equation proofs
• The analysis of elliptic families. I: Metrics and connections on determinant bundles
• The \(\zeta\)-determinant and \({\mathcal C}\)-determinant on the Grassmannian in dimension one
• The \(\zeta\)-determinant and the additivity of the \(\eta\)-invariant on the smooth, self-adjoint Grassmannian
• Families of Dirac operators, boundaries and the \(B\)-calculus
• Trace expansions for pseudodifferential boundary problems for Dirac-type operators and more general systems
• Determinants of Dirac boundary value problems over odd-dimensional manifolds
• Determinant bundles, manifolds with boundary and surgery
• ζ-determinant and the Quillen determinant on the Grassmannian of elliptic self-adjoint boundary conditions

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