Relative formulæ for the spectral invariants of the b-calculus and generalized APS boundary problems of Dirac operators

Paul Loya and Jinsung Park

Vol. 223 (2006), No. 2, 317–331

DOI: 10.2140/pjm.2006.223.317

Abstract

We relate zeta determinants of Dirac operators with generalized APS boundary conditions for compact manifolds with boundary and parallel b-zeta determinants of perturbed Dirac operators on the corresponding complete manifolds with cylindrical end. We also derive, without invertibility conditions, corresponding relative formulæ for the (b-) zeta determinants.

Keywords

Dirac operators, b-calculus, ζ-determinants

Mathematical Subject Classification 2000

Primary: 58J28

Secondary: 58J35, 58J20, 58J32

Milestones

Received: 5 July 2004

Revised: 10 October 2004

Accepted: 18 October 2004

Published: 1 February 2006