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- W1999158832 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." @default.
- W1999158832 created "2016-06-24" @default.
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- W1999158832 date "2011-11-15" @default.
- W1999158832 modified "2023-09-26" @default.
- W1999158832 title "The gluing formula of the refined analytic torsion for an acyclic Hermitian connection" @default.
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- W1999158832 doi "https://doi.org/10.1007/s00229-011-0504-3" @default.
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