Regularized determinants of Laplace type operators, analytic surgery and relative determinants

Details Regularized determinants of Laplace type operators, analytic surgery and relative determinants Regularized determinants of Laplace type operators, analytic surgery and relative determinants

2004-11-29

arxiv.org/abs/math/0411634v1

Mathematics

Differential Geometry

43 pages

Scientific paper

We study the asymptotic behaviour of regularized determinants of certain Laplace type operators with respect to singular deformations of the underlying manifold which are obtained by stretching a tubular neighborhood of an embedded separating hypersurface to a cylinder of infinite length. Using the asymptotic expansions, we derive adiabatic splitting formulas for regularized determinants of Laplace type operators.

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