Equivariant Cobordism of Flag Varieties and of Symmetric Varieties

TL;DR

This paper provides explicit descriptions of the equivariant cobordism rings for flag varieties and symmetric varieties, enabling new calculations and insights in algebraic geometry and cobordism theory.

Contribution

It offers explicit presentations of equivariant cobordism rings for flag and symmetric varieties, advancing computational tools in algebraic geometry.

Findings

Explicit presentation of equivariant cobordism ring of flag varieties

Borel presentation of the ordinary cobordism ring

Development of equivariant Schubert calculus in cobordism

Abstract

We obtain an explicit presentation of the equivariant cobordism ring of a complete flag variety. An immediate corollary is a Borel presentation of the ordinary cobordism ring. Another application is an equivariant Schubert calculus in cobordism. We also describe the rational cobordism rings of wonderful symmetric varieties of minimal rank.