2018
DOI: 10.2140/pjm.2018.294.401
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Smooth Schubert varieties and generalized Schubert polynomials in algebraic cobordism of Grassmannians

Abstract: We provide several ingredients towards a generalization of the Littlewood-Richardson rule from Chow groups to algebraic cobordism. In particular, we prove a simple product-formula for multiplying classes of smooth Schubert varieties with any Bott-Samelson class in algebraic cobordism of the grassmannian. We also establish some results for generalized Schubert polynomials for hyperbolic formal group laws. * The second author was supported by a public grant as part of the Investissement d'avenir project, referen… Show more

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Cited by 4 publications
(1 citation statement)
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“…Later, the interest shifted to Grassmann and flag bundles (cf. [13], [4], [12], [11], [10], [7], [8], [9]). One of the main difficulty of Schubert calculus in algebraic cobordism is caused by the fact that the fundamental classes of Schubert varieties are not well-defined in general oriented cohomology theories.…”
Section: Introductionmentioning
confidence: 99%
“…Later, the interest shifted to Grassmann and flag bundles (cf. [13], [4], [12], [11], [10], [7], [8], [9]). One of the main difficulty of Schubert calculus in algebraic cobordism is caused by the fact that the fundamental classes of Schubert varieties are not well-defined in general oriented cohomology theories.…”
Section: Introductionmentioning
confidence: 99%