齐次空间上的等变复结构及其共边性 班级

是 否 +2 论坛币

k人 参与回答

经管之家送您一份

应届毕业生专属福利!

求职就业群

赵安豆老师微信：zhaoandou666

经管之家联合CDA

送您一个全额奖学金名额~ !

立即领取

感谢您参与论坛问题回答

经管之家送您两个论坛币！

+2 论坛币

摘要翻译：
我们考虑紧齐次空间G/H，其中G是紧连通李群，H是它的最大秩闭连通子群。本文的目的是为在G/H上最大环面T^K的正则左作用下不变的复结构、几乎复结构和稳定复结构提供一种有效的泛环格计算方法。众所周知，在G/H上，我们可能有许多这样的结构，对于同一环面作用，用不动点计算它们的环面亏格，给出了在切空间中不动点处对应表示的t^k的权的可能集合的约束，以及在这些点处的符号的约束。在这种情况下，由于对任意一对这样的结构的权重和符号之间的关系的明确描述，还探讨了有效性。特别关注在群G的规范作用下不变的结构。利用经典结果，我们得到了这种情况下权和符号的显式描述。因此，我们用同调中的形式群律系数和上同调中的Chern数得到了这种结构的同调类的一个表达式。这些计算不需要关于流形G/H的上同调环的信息，但它们本身给出了该环中的重要关系。作为应用，我们给出了标志流形U(n)/t^n，Grassmann流形G_{n,k}=U(n)/(U(k)\乘U(n-k))的协边类和特征数的显式公式，并给出了一些有趣的例子。
---
英文标题：
《Equivariant complex structures on homogeneous spaces and their cobordism
  classes》
---
作者：
Victor M. Buchstaber, Svjetlana Terzic
---
最新提交年份：
2008
---
分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Topology        代数拓扑
分类描述：Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论，同调代数，流形的代数处理
--
一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
--

---
英文摘要：
  We consider compact homogeneous spaces G/H, where G is a compact connected Lie group and H is its closed connected subgroup of maximal rank. The aim of this paper is to provide an effective computation of the universal toric genus for the complex, almost complex and stable complex structures which are invariant under the canonical left action of the maximal torus T^k on G/H. As it is known, on G/H we may have many such structures and the computations of their toric genus in terms of fixed points for the same torus action give the constraints on possible collections of weights for the corresponding representations of T^k in the tangent spaces at the fixed points, as well as on the signs at these points. In that context, the effectiveness is also approached due to an explicit description of the relations between the weights and signs for an arbitrary couple of such structures. Special attention is devoted to the structures which are invariant under the canonical action of the group G. Using classical results, we obtain an explicit description of the weights and signs in this case. We consequently obtain an expression for the cobordism classes of such structures in terms of coefficients of the formal group law in cobordisms, as well as in terms of Chern numbers in cohomology. These computations require no information on the cohomology ring of the manifold G/H, but, on their own, give important relations in this ring. As an application we provide an explicit formula for the cobordism classes and characteristic numbers of the flag manifolds U(n)/T^n, Grassmann manifolds G_{n,k}=U(n)/(U(k)\times U(n-k)) and some particular interesting examples.
---
PDF链接：
https://arxiv.org/pdf/0801.3108

扫码加我 拉你入群

请注明：姓名-公司-职位

以便审核进群资格，未注明则拒绝

分享0 收藏0 回帖

关键词：computations coefficients Presentation Computation mathematics 计算 homogeneous 得到 环格 points