The ratio of two zeta-determinants of Dirac Laplacians associated with unitary involutions on a compact manifold with cylindrical end

2004/08/13 by Yoonweon Lee, Lee, Yoonweon
Mathematics · #58J50 #58J52 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.DG #math.SP #msc:58J50 #msc:58J52

paper · pdf · doi:10.48550/arxiv.math/0408175

23pages

arxiv created 2004/08/13 · openalex publication_date 2004/08/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given two unitary involutions σ₁ and σ₂ satisfying G σ_i = - σ_i G on ker B on a compact manifold with cylindrical end, M. Lesch, K. Wojciechowski ([LW]) and W. Müller ([M]) established the formula describing the difference of two eta-invariants with the APS boundary conditions associated with σ₁ and σ₂. In this paper we establish the analogous formula for the zeta-determinants of Dirac Laplacians. For the proof of the result we use the Burghelea-Friedlander-Kappeler's gluing formula for zeta-determinants and the scattering theory developed by W. Müller in [M]. This result was also obtained independently by J. Park and K. Wojciechowski ([PW2]).

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