Coefficients of the $\Sigma_3$-equivariant complex cobordism ring

TL;DR

This paper computes the coefficient ring of the equivariant Thom complex cobordism for the symmetric group on three elements, providing insights into methods for calculating related ring pullbacks in equivariant cobordism.

Contribution

It introduces a calculation of the equivariant cobordism ring for S_3 and discusses general techniques for ring pullback computations in equivariant cobordism.

Findings

Computed the coefficient ring for the S_3-equivariant complex cobordism.

Provided remarks on general methods for calculating ring pullbacks in equivariant cobordism.

Enhanced understanding of equivariant cobordism structures for symmetric groups.

Abstract

In this paper, we calculate the coefficient ring of equivariant Thom complex cobordism for the symmetric group on three elements. We also make some remarks on general methods of calculating certain pullbacks of rings which typically occur in calculations of equivariant cobordism.