Combinatorial presentations for algebraic cobordism rings of matroid toric varieties yield an isomorphism to Chow rings tensored with point cobordism, plus isomorphisms for wonderful varieties of hyperplane arrangements.
Algebraic Cobordism of Classifying Spaces
2 Pith papers cite this work. Polarity classification is still indexing.
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abstract
We define algebraic cobordism of classifying spaces, \Omega^*(BG) and G-equivariant algebraic cobordism \Omega^*_G(-) for a linear algebraic group G. We prove some properties of the coniveau filtration on algebraic cobordism, denoted F^j(\Omega^*(-)), which are required for the definition to work. We show that G-equivariant cobordism satisfies the localization exact sequence. We calculate \Omega^*(BG) for algebraic groups over the complex numbers corresponding to classical Lie groups GL(n), SL(n), Sp(n), O(n) and SO(2n+1). We also calculate \Omega^*(BG) when G is a finite abelian group. A finite non-abelian group for which we calculate \Omega^*(BG) is the quaternion group of order 8. In all the above cases, we check that \Omega^*(BG) is isomorphic to MU^*(BG).
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2026 2verdicts
UNVERDICTED 2representative citing papers
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.
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Algebraic cobordism rings of wonderful varieties and matroids
Combinatorial presentations for algebraic cobordism rings of matroid toric varieties yield an isomorphism to Chow rings tensored with point cobordism, plus isomorphisms for wonderful varieties of hyperplane arrangements.
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Motivic Segre classes of Schubert cells and the connective formal group law
A β-deformed version of motivic Segre classes of Schubert cells is constructed via the connective formal group law, with rational representatives via lattice models and structure constants via Knutson-Tao puzzles proven using quantum group intertwiners for d=1.