On the \(\eta\)-invariant of certain nonlocal boundary value problems

DOI10.1215/S0012-7094-99-09613-8zbMath0956.58014arXivdg-ga/9609001OpenAlexW1998131229MaRDI QIDQ1974887

Jochen Brüning, Matthias Lesch

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/dg-ga/9609001

zbMATH Keywords

eta invariantgluing lawAtiyah-Patodi-Singer boundary condition

Mathematics Subject Classification ID

Eta-invariants, Chern-Simons invariants (58J28) Boundary value problems on manifolds (58J32) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (26)

Zeta determinants on manifolds with boundary ⋮ Zeta and Fredholm determinants of self-adjoint operators ⋮ The BFK-gluing formula and relative determinants on manifolds with cusps ⋮ The relative eta invariant for a pair of Dirac-type operators on non-compact manifolds ⋮ Dai-Freed theorem and topological phases of matter ⋮ Refined analytic torsion as an element of the determinant line ⋮ Adiabatic decomposition of the \(\zeta\)-determinant and scattering theory ⋮ Relative index pairing and odd index theorem for even dimensional manifolds ⋮ The refined analytic torsion and a well-posed boundary condition for the odd signature operator ⋮ The gluing formula of the refined analytic torsion for an acyclic Hermitian connection ⋮ \(\eta \) forms and determinant lines ⋮ The multiplicative anomaly for determinants revisited; locality ⋮ The zeta-determinants of Dirac Laplacians with boundary conditions on the smooth, self-adjoint Grassmannian ⋮ Bulk-edge correspondence, spectral flow and Atiyah-Patodi-Singer theorem for the \(\mathcal{Z}_2\)-invariant in topological insulators ⋮ APS boundary conditions, eta invariants and adiabatic limits ⋮ An algebra of boundary value problems not requiring Shapiro-Lopatinskij conditions ⋮ The index formula and the spectral shift function for relatively trace class perturbations ⋮ On the gluing problem for the spectral invariants of Dirac operators ⋮ A new proof of the local regularity of the eta invariant of a Dirac operator ⋮ On boundary value problems for Dirac type operators. I: Regularity and self-adjointness ⋮ On gluing formulas for the spectral invariants of Dirac type operators ⋮ The Regularity of the Eta Function for Perturbations of Order -(dim X) of the Atiyah-Patodi-Singer Boundary Problem ⋮ SPECTRAL ASYMMETRY, ZETA FUNCTIONS, AND THE NONCOMMUTATIVE RESIDUE ⋮ On the gluing problem for Dirac operators on manifolds with cylindrical ends ⋮ Eta invariant and holonomy: the even dimensional case ⋮ ADIABATIC DECOMPOSITION OF THE -DETERMINANT OF THE DIRAC LAPLACIAN. I. THE CASE OF AN INVERTIBLE TANGENTIAL OPERATOR

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