Cohomology rings of the real and oriented partial flag manifolds

He Chen

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Cohomology rings of the real and oriented partial flag manifolds

机译：真实和定向部分旗歧管的同步圈

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摘要

We show, in contrast to the cases of complex and quaternionic partial flag manifolds, the rational cohomology rings of the real and oriented partial flag manifolds are generated not only by the characteristic classes of their canonical vector bundles, but also by exterior algebras arising from the rational cohomology rings of real Stiefel manifolds. We also discuss the rational and the mod-2 equivariant cohomology rings of these partial flag manifolds for certain canonical actions of tori and 2-tori. (C) 2020 Elsevier B.V. All rights reserved.

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《Topology and its applications》 |2020年第jul1期|107239.1-107239.25|共25页
作者
He Chen;
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作者单位

North China Elect Power Univ Dept Math & Phys Beijing Peoples R China;

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原文格式 PDF
正文语种 eng
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关键词
Flag manifold; Grassmannian; Stiefel manifold; Equivariant cohomology; Characteristic classes;

机译：国旗歧管;基层;Stiefel歧管;等式的同学;特征课程;

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1. Quantum cohomology of partial flag manifolds [J] . Buch AS Transactions of the American Mathematical Society . 2005,第2期

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2. Cohomology of smooth schubert varieties in partial flag manifolds [J] . V. Gasharov, V. Reiner The Journal of the London Mathematical Society . 2002,第3期

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3. QUANTUM COHOMOLOGY OF PARTIAL FLAG MANIFOLDS F-N1...(NK) [J] . Astashkevich A., Sadov V. Communications in Mathematical Physics . 1995,第3期

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4. Cohomology Rings of Oriented Seifert Manifolds with mod ps Coefficients [C] . J. Bryden NATO Advanced Research Workshop on New Techniques in Topological Quantum Field Theory . 2004

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5. The cohomology rings of seven dimensional primitive cohomogeneity one manifolds. [D] . Ultman, Shari K. 2009

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7. Flag Bott manifolds of general Lie type and their equivariant cohomology rings [O] . Shizuo Kaji, Shintarô Kuroki, Eunjeong Lee, 2020

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Cohomology rings of the real and oriented partial flag manifolds

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