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COBORDISM CLASSES OF FIBERINGS OVER PRODUCT OF PROJECTIVE SPACES

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Acta Mathematica Scientia 2009年第5期29卷 1421-1429页

作者：王彦英李京艳 College of Mathematics and Information Science Hebei Normal University Department of Mathematics and Physics Shijiazhuang Railway Institute

Let RP（k） denote the k-dimensional real projective space. This article determines which cobordism classes are represented by the total space of a fibering with prescribed base space RP（3）× RP（1）, RP（2） × RP... 详细信息

关键词： fibering characteristic number cobordism class

Two Commuting Involutions Fixing RP_(1)(2m+1)∪RP_(2)(2m+1)

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Chinese Annals of Mathematics,Series B 2021年第5期42卷 737-752页

作者： Suqian ZHAO Yanying WANG Jingyan LI School of Sciences Hebei University of Science and TechnologyShijiazhuang 050018China School of Mathematical Sciences Hebei Normal UniversityShijiazhuang 050024China

Let Z2 denote a cyclic group of 2 order and Z_(2)^(2)=Z_(2)×Z_(2)the direct product of *** that(M,Φ)is a closed and smooth manifold M with a smooth Z_(2)^(2)-action whose fixed point set is the disjoint union of two real projective spaces with the same *** this paper,the authors give a sufficient condition on the fixed data of the action for(M,Φ)bounding equivariantly.

关键词： Z_(2)^(2)-action Fixed data characteristic number Simultaneous bordism Stiefel-Whitney class

Fiberings with Fiber RP(k)

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Acta Mathematica Sinica,English Series 2005年第5期21卷 997-1000页

作者： Zuo LIU Zhen De WU Department of Mathematics Hebei Normal University Shijiazhuang 050016 P. R. China

Let κ be non-negative integer. The unoriented bordism classes, which can be represented as [RP（ξ^κ）] where ξ^κ is a k-plane bundle, form an ideal of the unoriented bordism ring MO.. A group of generators of this ideal expressed by a base of MO. and a necessary and sufficient condition for a bordism class to belong to this ideal are given.

关键词： Bordism classes characteristic number Fibering Partition

From a projective invariant to some new properties of algebraic hypersurfaces

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Science China Mathematics 2014年第11期57卷 2273-2284页

作者： LUO ZhongXuan ZHOU XinChen GU David XianFeng School of Mathematical Sciences Dalian University of Technology School of Software Dalian University of Technology Department of Computer Science State University of New York at Stony Brook

Projective invariants are not only important objects in mathematics especially in geometry,but also widely used in many practical applications such as in computer vision and object recognition. In this work,we show a projective invariant named as characteristic number,from which we obtain an intrinsic property of an algebraic hypersurface involving the intersections of the hypersurface and some lines that constitute a closed loop. From this property,two high-dimensional generalizations of Pascal's theorem are given,one establishing the connection of hypersurfaces of distinct degrees,and the other concerned with the intersections of a hypersurface and a simplex.

关键词： characteristic number algebraic hypersurfaces Pascal's theorem characteristic mapping simplex