Acta Scientiarum Naturalium Universitatis Pekinensis

Previous Articles     Next Articles

Intersection Theory on Homogeneous Spaces of Simple Lie Group

BAO Zhiqiang   

  1. Department of Mathematics, School of Mathematical Sciences, Peking University, Beijing, 100871
  • Received:1998-04-01 Online:1999-05-20 Published:1999-05-20

单李群齐性空间中的相交理论

包志强   

  1. 北京大学数学学院数学系,北京,100871

Abstract: Consider H*(Un/Tn, Z), the integral cohomology ring of homogeneous space Un/Tn. It is a quotient ring of the polynomial ring in n variables. Particularly, the homogeneous part with degree d=dimUn/Tn corresponds to the highest dimensional cohomology group Z, i.e., each degree d homogeneous polynomial f corresponds to an integer χ(f). The present article computes this correspondence explicitly. The connections with the intersection theory of the manifold Un/Tn are also discussed. Similar result applies to the homogeneous space Spn/Tn.

Key words: homogeneous space, intersection theory, intersection number

摘要: 考虑齐性空间Un/Tn的整系数上同调环H*(Un/Tn , Z)。它是n元多项式环的一个商环。特别地,商环的d=dimUn/Tn次齐次部分对应于顶维上同调群Z,即每个d次齐次多项式 f都对应于一个整数 χ(f)。本文具体计算出了此对应。在几何上,这一对应给出了到Un/Tn的连续映射的相交数的计算方法。同样的方法也适用于Spn/Tn上的相交理论的研究。

关键词: 齐性空间, 相交理论, 相交数

CLC Number: