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## Chern classes of reductive groups and an adjunction formula

Annales de l'Institut Fourier. 2006. Vol. 56. No. 4. P. 1225-1256.

In this paper, I construct noncompact analogs of the Chern classes of equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the Euler characteristic of complete intersections in reductive groups. When a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. An extension of these results to arbitrary spherical homogeneous spaces is outlined. This is the first step towards extension to the reductive case of the explicit answer given by D.Bernstein, Khovanskii and Kouchnirenko for the Euler characteristic of all complete intersections in the complex torus (C^*)^n.