The gluing formula of the refined analytic torsion for an acyclic Hermitian connection |
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Authors: | Rung-Tzung Huang Yoonweon Lee |
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Affiliation: | 1. Department of Mathematics, National Central University, Chung-Li, 320, Taiwan, Republic of China 2. Department of Mathematics, Inha University, Incheon, 402-751, Korea
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Abstract: | In the previous study by Huang and Lee (arXiv:1004.1753) we introduced the well-posed boundary conditions ${{mathcal P}_{-, {mathcal L}_{0}}}$ and ${{mathcal P}_{+, {mathcal L}_{1}}}$ for the odd signature operator to define the refined analytic torsion on a compact manifold with boundary. In this paper we discuss the gluing formula of the refined analytic torsion for an acyclic Hermitian connection with respect to the boundary conditions ${{mathcal P}_{-, {mathcal L}_{0}}}$ and ${{mathcal P}_{+, {mathcal L}_{1}}}$ . In this case the refined analytic torsion consists of the Ray-Singer analytic torsion, the eta invariant and the values of the zeta functions at zero. We first compare the Ray-Singer analytic torsion and eta invariant subject to the boundary condition ${{mathcal P}_{-, {mathcal L}_{0}}}$ or ${{mathcal P}_{+, {mathcal L}_{1}}}$ with the Ray-Singer analytic torsion subject to the relative (or absolute) boundary condition and eta invariant subject to the APS boundary condition on a compact manifold with boundary. Using these results together with the well known gluing formula of the Ray-Singer analytic torsion subject to the relative and absolute boundary conditions and eta invariant subject to the APS boundary condition, we obtain the main result. |
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