A Cheeger-Mueller theorem for symmetric bilinear torsions

Details A Cheeger-Mueller theorem for symmetric bilinear torsions A Cheeger-Mueller theorem for symmetric bilinear torsions

2006-10-19

arxiv.org/abs/math/0610577v1

Chinese Annals of Mathematics, 29B (2008), 385-424.

Mathematics

Differential Geometry

48 pages

Scientific paper

We generalize a theorem of Bismut-Zhang, which extends the Cheeger-Mueller theorem on Ray-Singer torsion and Reidemeister torsion, to the case where the flat vector bundle over a closed manifold carries a nondegenerate symmetric bilinear form. As a consequence, we prove the Burghelea-Haller conjecture which gives an analytic interpretation of the Turaev torsion. It thus also provides an analytic interpretation of (not merely the absolute value of) the Alexander polynomial in knot theory.

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