The gluing formula of the zeta-determinants of Dirac Laplacians for certain boundary conditions

zbMath1408.58026arXiv1311.4281MaRDI QIDQ491469

Yoonweon Lee, Rung-Tzung Huang

Publication date: 25 August 2015

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.4281

Mathematics Subject Classification ID

Spectral problems; spectral geometry; scattering theory on manifolds (58J50) Eta-invariants, Chern-Simons invariants (58J28) Determinants and determinant bundles, analytic torsion (58J52)

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Cites Work

• The comparison of two constructions of the refined analytic torsion on compact manifolds with boundary
• The gluing formula of the refined analytic torsion for an acyclic Hermitian connection
• Refined analytic torsion as an element of the determinant line
• Refined analytic torsion on manifolds with boundary
• Mayer-Vietoris type formula for determinants of elliptic differential operators
• The \(\zeta\)-determinant and the additivity of the \(\eta\)-invariant on the smooth, self-adjoint Grassmannian
• The \(\zeta\)-determinant and Quillen determinant for a Dirac operator on a manifold with boundary
• Zeta determinants on manifolds with boundary
• The refined analytic torsion and a well-posed boundary condition for the odd signature operator
• Zero sets of solutions to semilinear elliptic systems of first order
• Trace expansions for pseudodifferential boundary problems for Dirac-type operators and more general systems
• Determinants of Dirac boundary value problems over odd-dimensional manifolds
• The zeta-determinants of Dirac Laplacians with boundary conditions on the smooth, self-adjoint Grassmannian
• Refined analytic torsion
• On the gluing problem for the spectral invariants of Dirac operators
• Unique continuation in geometry
• Burghelea-Friedlander-Kappeler’s gluing formula for the zeta-determinant and its applications to the adiabatic decompositions of the zeta-determinant and the analytic torsion
• The [eta-invariant, Maslov index, and spectral flow for Dirac-type operators on manifolds with boundary]
• On gluing formulas for the spectral invariants of Dirac type operators
• Poincar\'e--Reidemeister metric, Euler structures, and torsion