Absolute torsion and eta-invariant

Details Absolute torsion and eta-invariant Absolute torsion and eta-invariant

1999-03-23

arxiv.org/abs/math/9903141v1

Mathematics

Differential Geometry

10 pages

Scientific paper

In a recent joint work with V. Turaev (cf. math.DG/9810114) we defined a new concept of combinatorial torsion which we called absolute torsion. Compared with the classical Reidemeister torsion it has the advantage of having a well-defined sign. Also, the absolute torsion is defined for arbitrary orientable flat vector bundles, and not only for unimodular ones, as is classical Reidemeister torsion. In this paper I show that the sign behavior of the absolute torsion, under a continuous deformation of the flat bundle, is determined by the eta-invariant and the Pontrjagin classes.

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