Abstract
We present a short analytic proof of the equality between the analytic and combinatorialtorsion. We use the same approach as in the proof given by Burghelea, Friedlander andKappeler, but avoid using the difficult Mayer-Vietoris type formula for the determinantsof elliptic operators. Instead, we provide a direct way of analyzing the behaviour of thedeterminant of the Witten deformation of the Laplacian. In particular, we show that thisdeterminant can be written as a sum of two terms, one of which has an asymptoticexpansion with computable coefficients and the other is very simple (no zeta-functionregularization is involved in its definition).
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Braverman, M. New Proof of the Cheeger–Müller Theorem. Annals of Global Analysis and Geometry 23, 77–92 (2003). https://doi.org/10.1023/A:1021227705930
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DOI: https://doi.org/10.1023/A:1021227705930