Thom form in equivariant Cech-de Rham theory

الأصل · EN

In the present paper, we provide the foundation of a G-equivariant Cech-de Rham theory for a compact Lie group G by using the Cartan model of equivariant differential forms. Our approach is quite elementary without referring to the Mathai-Quillen framework. In particular, by a direct computation, we give an explicit formula of the U(l)-equivariant Thom form of Cˡ, which deforms the classical Bochnor-Martinelli kernel. Also we discuss a version of equivariant Riemann-Roch formula.