On the uniqueness problem of bivariant Chern classes

Abstract

In this paper we show that the bivariant Chern class $\gamma :\mathbb{F}\to \mathbb{H}$ for morphisms from possibly singular varieties to nonsingular varieties are uniquely determined, which therefore implies that the Brasselet bivariant Chern class is unique for cellular morphisms with nonsingular target varieties. Similarly we can see that the Grothendieck transformation $\tau :{\mathbb{K}}_{alg}\to {\mathbb{H}}_{\mathbb{Q}}$ constructed by Fulton and MacPherson is also unique for morphisms with nonsingular target varieties.