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Quillen's relative Chern character is multiplicative

Paul-Emile Paradan·Michèle Vergne
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Abstract

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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Paul-Emile Paradan, Michèle Vergne. 2008-09-26. Quillen's relative Chern character is multiplicative. https://arxiv.org/abs/math/0702575

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