Equivariant Cobordism of Flag Varieties and of Symmetric Varieties
Valentina Kiritchenko, Amalendu Krishna

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.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology
