| 二次图构形的边搜索法及其Orlik-Solomon代数的上同调 |
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| 引用本文： | 晏清照,沈晓飞,张现仁,姜广峰.二次图构形的边搜索法及其Orlik-Solomon代数的上同调[J].数学进展,2011(3). |
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| 作者姓名： | 晏清照 沈晓飞 张现仁 姜广峰 |
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| 作者单位： | 北京化工大学理学院;北京化工大学化学工程学院; |
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| 基金项目： | 国家自然科学基金(No.10671009). |
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| 摘 要： | 本文研究了一类特殊的图构形,即二次图构形.首先,给出了弦图的边搜索法,用边搜索法可以决定弦图所对应的超平面构形中超平面的哪些排序使构形是二次均.其次,对二次图构形的Orlik-Solomon代数作为线性空间的维数进行了计算,得到了它的Poincare多项式的表达式.最后,对二次图构形Orlik-Solomon代数的上同调进行了研究,对边缘算子集中在秩为二的模元时,得到了二次图构形的Orlik-Solomon代数的上同调的维数计算公式.
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| 关 键 词： | 边搜索法 二次图构形 OS代数 上同调 |
Edge Searching Algorithm for Quadratic Graphic Arrangements and the Cohomology of Orlik-Solomon Algebras |
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| YAN Qingzhao,SHEN Xiaofei,ZHANG Xianren,JIANG Guangfeng.Edge Searching Algorithm for Quadratic Graphic Arrangements and the Cohomology of Orlik-Solomon Algebras[J].Advances in Mathematics,2011(3). |
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| Authors: | YAN Qingzhao SHEN Xiaofei ZHANG Xianren JIANG Guangfeng |
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| Institution: | YAN Qingzhao~1,SHEN Xiaofei~1,ZHANG Xianren~2,JIANG Guangfeng~1 (1.School of Science,Beijing University of Chemical Technology,Beijing,100029,P.R.China,2.College of Chemical Engineering,P.R. China) |
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| Abstract: | A special class of graphic arrangements,quadratic graphic arrangements,is studied.The edge searching algorithm is formulated and used to determine which order of the hyperplanes in a graphic arrangement makes the arrangement quadratic.The Poincare polynomials of the Orlik-Solomon algebras for this class of arrangements are formulated.When the boundary operator is concentrated in a rank two element of the intersection lattice,a dimension formula of the cohomology of the Orlik-Solomon algebras for the quadrat... |
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| Keywords: | edge searching algorithm quadratic graphic arrangement Orlik-Solomon algebras cohomology |
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