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Morse theory and higher torsion invariants II

Sebastian Goette
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Abstract

Let p: M -> B be a family of compact manifolds equipped with a unitarily flat vector bundle F -> M. We generalize Igusa's higher Franz-Reidemeister torsion τ(M/B;F) to the case that the fibre-wise cohomology H^*(M/B;F) -> B carries a parallel metric. If moreover M admits a fibre-wise Morse function, we compute the difference of τ(M/B;F) and the higher analytic torsion \Cal T(M/B;F). We also generalise the examples given in math.DG/0111222 .

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Sebastian Goette. 2003-05-20. Morse theory and higher torsion invariants II. https://arxiv.org/abs/math/0305287

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