We consider a compact manifold with a piece isometric to a (finite-length) cylinder. By making the length of the cylinder tend to infinity, we obtain an asymptotic gluing formula for the zeta determinant of the Hodge Laplacian and an asymptotic expansion of the torsion of the corresponding long exact sequence of cohomology equipped with $L^2$-metrics. As an application, we give a purely analytic proof of the gluing formula for analytic torsion.

中文翻译：

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散射矩阵和解析扭转

我们考虑一个紧凑的歧管，它与（有限长）圆柱体等轴测。通过使圆柱的长度趋于无穷大，我们获得了Hodge Laplacian的zeta行列式的渐近粘合公式，以及配备有${\mathrm{大号}}^2$-指标。作为应用，我们给出了用于分析扭转的胶粘公式的纯粹分析证明。