A note on the equivariant formal group law of the equivariant complex cobordism ring

TL;DR

This paper computes the $G$-equivariant formal group law associated with the $G$-equivariant complex cobordism spectrum for finite abelian groups, advancing understanding of equivariant formal group laws.

Contribution

It provides an explicit computation of the equivariant formal group law for finite abelian groups, a previously less-understood aspect of equivariant complex cobordism.

Findings

Explicit formula for the $G$-equivariant formal group law.

Enhanced understanding of the structure of equivariant complex cobordism.

Foundation for further studies in equivariant stable homotopy theory.

Abstract

For a finite abelian group $G$, we compute the $G$-equivariant formal group law corresponding to the $G$-equivariant complex cobordism spectrum with its canonical complex orientation.