Morse theory and higher torsion invariants II

2003/05/20 by Sebastian Goette, Goette, Sebastian · 4 citations
Mathematics · #57Q10 #57R22 #58J52 #Advanced Operator Algebra Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT) #math.DG #math.KT #msc:57Q10 #msc:57R22 #msc:58J52

paper · pdf · doi:10.48550/arxiv.math/0305287

amstex (with pstricks), 77 pages. For minor updates, see http://www.mathematik.uni-regensburg.de/Goette/preprints/

arxiv created 2003/05/20 · openalex publication_date 2003/05/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 .

Cited by

• Exotic smooth structures on topological fibre bundles II
• Metrics of positive scalar curvature and generalised Morse functions, part 1
• A comparison between the Bismut-Lott torsion and the Igusa-Klein torsion
• Equivalence of higher torsion invariants

Related

• Morse theory and higher torsion invariants I
• Comparison of Higher Smooth Torsion
• Generalized Morse Functions, Excision and Higher Torsions
• Exotic smooth structures on topological fibre bundles I
• A comparison between the Bismut-Lott torsion and the Igusa-Klein torsion