The equivariant complex cobordism ring of a finite abelian group

TL;DR

This paper computes the equivariant complex cobordism ring for finite abelian groups, advancing understanding of equivariant stable homotopy theory and cobordism invariants.

Contribution

It provides the first explicit computation of the equivariant complex cobordism ring for all finite abelian groups.

Findings

Explicit description of (MU_G)_* for finite abelian G

New algebraic structures identified in the cobordism ring

Framework established for future equivariant cobordism computations

Abstract

We compute the equivariant (stable) complex cobordism ring $(MU_G)_*$ for finite abelian groups $G$.