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Thom form in equivariant Čech–de Rham theory

2018; World Scientific; Volume: 29; Issue: 08 Linguagem: Inglês

10.1142/s0129167x18500507

1793-6519

Ko Fujisawa,

Advanced Algebra and Geometry

In the present paper, we provide the foundation of a [Formula: see text]-equivariant Čech–de Rham theory for a compact Lie group [Formula: see text] 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 [Formula: see text]-equivariant Thom form of [Formula: see text], which deforms the classical Bochnor–Martinelli kernel. Also, we discuss a version of equivariant Riemann–Roch formula.