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Regularized determinants of Laplace-type operators, analytic surgery, and relative determinants. (English) Zbl 1111.58026

The authors study the behaviour of regularized determinants of Laplace type-operators with respect to certain singular deformations which are related to analytic surgery. This is a method developed by Mazzeo and Melrose to study the behaviour of global spectral invariants of Dirac- and Laplace operators with respect to decompositions of the underlying Riemannian manifolds. The results obtained generalize previous ones by other authors. In particular some of these are related to a work by J.-M. Bismut and J.-B. Bost [Acta Math. 165, No. 1/2, 1–103 (1990; Zbl 0709.32019)].

MSC:

58J52 Determinants and determinant bundles, analytic torsion
58J50 Spectral problems; spectral geometry; scattering theory on manifolds

Citations:

Zbl 0709.32019
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References:

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