Morse theory and higher torsion invariants I

• DOI: 10.48550/arxiv.math/0111222
• Publication Date: 2001-01-01
• Authors: Goette, Sebastian
• Keywords: Mathematics - Differential Geometry; Differential Geometry (math.DG); Mathematics - K-Theory and Homology; FOS: Mathematics; 58J52; K-Theory and Homology (math.KT); 58J52; 57R22, 57Q10; 0101 mathematics; 01 natural sciences; 57R22, 57Q10

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 ��(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 ��(M/B;F) and the higher analytic torsion \Cal T(M/B;F). We also generalise the examples given in math.DG/0111222 .<br/>amstex (with pstricks), 77 pages. For minor updates, see http://www.mathematik.uni-regensburg.de/Goette/preprints/<br/>