Combinatorial Formulas for Products of Thom Classes
Combinatorial Formulas for Products of Thom Classes
复制标题
Thom 类乘积的组合公式
DOI：
10.1007/0-387-21791-6_12
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
Catalin Zara
中科院分区：
文献类型：
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作者：
V. Guillemin;Catalin Zara
设一个维数为11,1的环面，取一个有限的紧哈密顿流形。circleS1inGisgenericifMG = MS1。对于这样一个圆，与其作用有关的矩映射是一个完美的莫尔斯函数。让{Wp +;p∈MG}为与此函数相关的m的Morse-Whitney分层，设τp+为等变Thom类对偶toWp+。这些类构成了hg *(M)作为模块的基础，特别是与。对于一大类这类流形，我们得到了τp+s的组合描述，并由此得到了cpgr的组合公式。
LetGbe a torus of dimensionn>1 andMbe a compact HamiltonianG-manifold withMGfinite. A circleS1inGisgenericifMG=MS1. For such a circle the moment map associated with its action onMis a perfect Morse function. Let {Wp+;p∈MG} be the Morse-Whitney stratification ofMassociated with this function and let τp+be the equivariant Thom class dual toWp+. These classes form a basis ofHG*(M) as a module overand, in particular,with. For a large class of manifolds of this type we obtain a combinatorial description of these τp+s and, from this description, a combinatorial formula forcpgr.