Morse theory and higher torsion invariants I

Details Morse theory and higher torsion invariants I Morse theory and higher torsion invariants I

2001-11-20

arxiv.org/abs/math/0111222v3

Mathematics

Differential Geometry

80 pages, AmSTeX, uses pstricks. v2: new abstract, more examples and applications. v3: 94 pages, major revision, submitted; Th

Scientific paper

We compare the higher analytic torsion of Bismut and Lott of a fibre bundle p: M -> B equipped with a flat vector bundle F -> M and a fibre-wise Morse function h on M with a higher torsion T that is constructed in terms of a families Thom-Smale complex associated to h and F, thereby extending previous joint work with Bismut. Under additional conditions on F, the torsion T is related to Igusa's higher Franz-Reidemeister torsion. As an application, we use the higher analytic torsion to detect infinite families of smooth bundles p_i: M -> B with diffeomorphic fibres that are homeomorphic but not diffeomorphic as bundles.

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