| 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,2017,38(4):461~468 |
| Kac-Moody群及其旗流形的庞加莱级数 和有理同伦型 |
| Poincar\'e Series and Rational Homotopy Types of Kac-Moody Groups and Their Flag Manifolds |
| Received:January 21, 2015 Revised:January 02, 2017 |
| DOI：10.16205/j.cnki.cama.2017.0007 |
| 中文关键词: Kac-Moody group, Flag manifold, Poincar |
| 英文关键词:Kac-Moody group, Flag manifold, Poincar |
| 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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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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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