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

Yoonweon Lee
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Abstract

Given two unitary involutions $σ_{1}$ and $σ_{2}$ 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 $σ_{1}$ and $σ_{2}$. 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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Yoonweon Lee. 2004-08-13. The ratio of two zeta-determinants of Dirac Laplacians associated with unitary involutions on a compact manifold with cylindrical end. https://arxiv.org/abs/math/0408175

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