Higher analytic torsion of sphere bundles and continuous cohomology of $Diff(S^{2n-1})$

Details Higher analytic torsion of sphere bundles and continuous cohomology of $Diff(S^{2n-1})$ Higher analytic torsion of sphere bundles and continuous cohomology of $Diff(S^{2n-1})$

1998-02-20

arxiv.org/abs/math/9802100v1

Mathematics

Differential Geometry

10 pages

Scientific paper

Using the higher analytic torsion form of Bismut and Lott we construct a
characteristic class for smooth sphere bundles. We calculate this class in the
case where the sphere bundle comes from a complex vector bundle. Related to
these characteristic classes we define nontrivial continuous group cohomology
classes of the diffeomorphism group of odd dimensional spheres.

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