η-invariant and flat vector bundles II

Details η-invariant and flat vector bundles II η-invariant and flat vector bundles II

2006-04-16

arxiv.org/abs/math/0604357v2

Mathematics

Differential Geometry

Modified Remark 3.4

Scientific paper

We first apply the method and results in the previous paper to give a new proof of a result (hold in $ {\bf C}/{\bf Z}$) of Gilkey on the variation of h-invariants associated to non self-adjoint Dirac type operators. We then give an explicit local expression of certain h-invariant appearing in recent papers of Braverman-Kappeler on what they call refined analytic torsion, and propose an alternate formulation of their definition of the refined analytic torsion. A refinement in ${\bf C}$ of the above variation formula is also proposed.

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