| Kac-Moody群及其旗流形的庞加莱级数和有理同伦型 |
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| 引用本文： | 赵旭安,金春花,张继敏.Kac-Moody群及其旗流形的庞加莱级数和有理同伦型[J].数学年刊A辑(中文版),2017,38(4):461-468. |
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| 作者姓名： | 赵旭安 金春花 张继敏 |
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| 作者单位： | 淮阴师范学院数学科学学院, 江苏 淮安 223001.,淮阴师范学院数学科学学院, 江苏 淮安 223001.,淮阴师范学院数学科学学院, 江苏 淮安 223001. |
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| 基金项目： | 本文受到国家自然科学基金(No.11571038)的资助. |
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| 摘 要： | 研究了不定型的Kac-Moody群及其旗流形的有理上同调.通过从庞加莱级数提取关于同调的信息,能够决定Kac-Moody群及其旗流形的有理上同调环.因为这些空间都是有理formal的空间,也决定了它们的有理同伦群及有理同伦型.
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| 关 键 词： | Kac-Moody group Flag manifold Poincar |
| 收稿时间： | 2015/1/21 0:00:00 |
| 修稿时间： | 2017/1/2 0:00:00 |
Poincar\'e Series and Rational Homotopy Types of Kac-Moody Groups and Their Flag Manifolds |
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| ZHAO Xu''an,JIN Chunhua and ZHANG Jimin.Poincar\'e Series and Rational Homotopy Types of Kac-Moody Groups and Their Flag Manifolds[J].Chinese Annals of Mathematics,2017,38(4):461-468. |
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| Authors: | ZHAO Xu'an JIN Chunhua and ZHANG Jimin |
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| Institution: | School of Mathematics, Beijing Normal University,Beijing 100875, China.,Science and Technology on Information Assurance Laboratory, Beijing 100072, China. and Tianjin Baodi Specialized Secondary School, Tianjin 301800, China. |
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| Abstract: | In this paper, the authors study the rational cohomology rings of indefinite Kac-Moody groups and their flag manifolds.
By extracting the information of cohomology from the Poincar\''{e} series,
the rational cohomology rings of these spaces can be determined.
Since Kac-Moody groups and their flag manifolds are rational formal,
the authors also determine the rational homotopy groups and rational homotopy types. |
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| Keywords: | Kac-Moody group Flag manifold Poincar |
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