Classification of compact transformation groups on cohomology complex projective spaces with codimension one orbits
Classification of compact transformation groups on cohomology complex projective spaces with codimension one orbits
复制标题
余维一轨道上同调复射影空间上紧变换群的分类
DOI：
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发表时间：
1977
期刊：
影响因子：
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通讯作者：
F. Uchida
中科院分区：
文献类型：
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作者：
F. Uchida
H. C. Wang[16]在D. Montgomery-H完全分类了球上紧连通李群的传递作用后，研究了余维为1轨道的球上的紧变换群。Samelson [1]， A. Borel[1]等。研究了有理上同调复射影空间上的相似问题。设G为紧连通李群，M为单连通有理上同调复射影n空间，其中G作用于一个余维1轨道上。本文的目的是对这样的对（G， M）进行基本同构的分类。这里我们说
H. C. Wang [16] investigated compact transformation groups on spheres with codimension one orbits, after the classification of transitive actions of compact connected Lie groups on spheres was done completely by D. Montgomery-H. Samelson [12], A. Borel [1] and others. In this paper we study similar problem on rational cohomology complex projective spaces. Let G be a compact connected Lie group and let M be a simply connect ed rational cohomology complex projective n-space on which G acts differ entiably with a codimension one orbit. The purpose of this paper is to classify such pairs (G, M) up to essentially isomorphism. Here we say that