New proof of the Cheeger-Muller Theorem

Details New proof of the Cheeger-Muller Theorem New proof of the Cheeger-Muller Theorem

2001-12-04

arxiv.org/abs/math/0112040v2

Mathematics

Differential Geometry

13 pages, more details are given in section 5, some misprints are corrected

Scientific paper

We present a short analytic proof of the equality between the analytic and combinatorial torsion. We use the same approach as in the proof given by Burghelea, Friedlander and Kappeler, but avoid using the difficult Mayer-Vietoris type formula for the determinants of elliptic operators. Instead, we provide a direct way of analyzing the behaviour of the determinant of the Witten deformation of the Laplacian. In particular, we show that this determinant can be written as a sum of two terms, one of which has an asymptotic expansion with computable coefficients and the other is very simple (no zeta-function regularization is involved in its definition).

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