Quillen's relative Chern character is multiplicative

Details Quillen's relative Chern character is multiplicative Quillen's relative Chern character is multiplicative

2007-02-20

arxiv.org/abs/math/0702575v3

Mathematics

Differential Geometry

28 pages. This article will appear in the proceedings of the conference "Algebraic Analysis and Around" in honour of Professor

Scientific paper

In the 80's, Quillen constructed a de Rham relative cohomology class associated to a smooth morphism between vector bundles, that we call the relative Quillen Chern character. In the first part of this paper we prove the multiplicativ property of the relative Quillen Chern character. Then we obtain a Riemann-Roch formula between the relative Chern character of the Bott morphism and the relative Thom form.

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