摘要翻译：
第二作者研究了两实齐次同轴二次曲面的交的拓扑结构，证明了它与单位球面的交在大多数情况下是差胚于球面积的连通和。本文将这种方法与Antony Bahri、Martin Bendersky、Fred Cohen和第一作者的一种新方法相结合，研究了K>2二次曲面的交点，并给出了一类与球积的连通和微分同胚的非常一般的流形族。其中包括由Frederic Bosio和Laurent Meerseman推测结果的矩角流形。作为副产物，对K=2的情形给出了更简单、更简洁的证明。两个新的部分包含了本文第一版中未包含的结果：第二部分描述了流形在切去相关多面体的顶点或边后的拓扑变化，这些变化可以以一种特殊的方式与previos的结果相结合，产生新的无穷多个流形族，这些流形族是球积的连通和。在其他情况下，我们得到稍微复杂一点的流形：由此，我们解决了Bosio-Meerseman关于与截断立方体相关的流形的另一个问题。在第3节中，我们利用这一点证明了矩角流形的上同调积的已知规则在一般情况下必须被彻底修正。我们声明修改后的规则，但将详细信息留给另一个发布。第0节回顾已知的定义和结果，在第2.1节中定义和探讨了一些基本拓扑结构。在附录中，我们陈述并证明了在第1和第2节中使用的关于特殊可微流形的一些结果。
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英文标题：
《Intersections of Quadrics, Moment-angle Manifolds and Connected Sums》
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作者：
Samuel Gitler and Santiago Lopez de Medrano
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最新提交年份：
2012
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分类信息：

一级分类：Mathematics        数学
二级分类：Geometric Topology        几何拓扑
分类描述：Manifolds, orbifolds, polyhedra, cell complexes, foliations, geometric structures
流形，轨道，多面体，细胞复合体，叶状，几何结构
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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
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英文摘要：
  The topology of the intersection of two real homogeneous coaxial quadrics was studied by the second author who showed that its intersection with the unit sphere is in most cases diffeomorphic to a connected sum of sphere products. Combining that approach with a recent one (due to Antony Bahri, Martin Bendersky, Fred Cohen and the first author) we study here the intersections of k>2 quadrics and we identify very general families of such manifolds that are diffeomorphic to connected sums of sphere products. These include those moment-angle manifolds for which the result was conjectured by Frederic Bosio and Laurent Meersseman. As a byproduct, a simpler and neater proof of the result for the case k=2 is obtained.   Two new sections contain results not included in the first version of this article: Section 2 describes the topological change on the manifolds after the operations of cutting off a vertex or an edge of the associated polytope, which can be combined in a special way with the previos results to produce new infinite families of manifolds that are connected sums of sphere products. In other cases we get slightly more complicated manifolds: with this we solve another question by Bosio-Meersseman about the manifold associated to the truncated cube.   In Section 3 we use this to show that the known rules for the cohomology product of a moment-angle manifold have to be drastically modified in the general situation. We state the modified rule, but leave the details of this for another publication.   Section 0 recalls known definitions and results and in section 2.1 some elementary topological constructions are defined and explored. In the Appendix we state and prove some results about specific differentiable manifolds, which are used in sections 1 and 2.
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PDF链接：
https://arxiv.org/pdf/0901.2580