Algebraic Topology

In a class having discussion on Graphs and Algebraic Topology ( 1998), Prof.

在组合拓扑讨论班上（1998）。

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Algebraic Topology; Symplectic Geometry and Topology; Ordinary and Partial Differential Equations.

代数拓扑；辛几何与拓扑；常微分和偏微分方程。

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Knowledge of elementary algebraic topology and elementary differential geometry is recommended, but not required.

建议事先知道一些关于代数拓扑和微分几何的基本知识，但不是必需的。

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Some more advanced algebraic topology may also be useful as might some knowledge of category theory.

更深入的代数拓扑学以及范畴理论的知识将有更大的帮助.

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An identification edge structure is put forward to represent non manifold modeling, which is built on the concepts and methods of the complex and CW complex in algebraic topology.

提出了一个非流形结构的表示方法&粘合边结构，其数学基础是代数拓扑中的复形理论。

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On Geographical Science In algebraic topology, J.

在代数拓扑学中J。

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Used the theorem of exponential correspondence, a theorem on quotient map was generalized to the cases of coinduced topology, and some applications of it in algebraic topology were also discussed.

利用指数对应定理，将关于商映射的一个定理推广到上诱导拓扑的情形，并给出其在代数拓扑学中的若干应用。

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This paper makes an extension of the map from a sphere into an euclidean space to the mapof a sphere into a smooth manifold by means of the cyclic transformation theory of algebraic topology, gaining Borsuk-Ulam type of theorem.

应用代数拓扑学中周期变换的理论，将球面到欧氏空间的映射推广到从球面到光滑流形映射的情形，从而得到了Brosuk－Ulam型定理。

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The Lefschetz fixed-point theorem ( and the Nielsen fixed-point theorem) from algebraic topology is notable because it gives, in some sense, a way to count fixed points.

在博拉奇不动点定理中给出了一般标准：如果不满意迭代函数程序就产生一个固定点。

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In algebraic topology, ones pay much attention to not only the existence of the coincidence points but also the estimation of their number and classification.

在代数拓扑学中，人们不仅对重合点的存在感兴趣，也十分关注重合点的个数估计以及重合点的分类情况。

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You have a basic understanding of differential calculus and at least one year of algebraic topology?

你们都对微积分有基本认识并至少学过一年代数拓扑吧

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Brouwer's fixed point theorem is shown to make use Of the knowledge of Point set Topology but not to make use of the knowledge of Algebraic Topology.

文章没有利用代数拓扑知识，而是利用点集拓扑知识证明了Brouwer不动点定理。

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An application of algebraic topology

代数拓扑的一个应用

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Inspired by the methods in algebraic topology, we invented an algorithm, which can efficiently reduce the genus, and we can find a quasi-planar graph embedding.

受到代数拓扑的启发，我们发明了一个算法，可以高效单调的减少图嵌入曲面的亏格，并可寻找到称为拟平面图的拓扑曲面。

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They are studied for their global properties by the methods of algebra and algebraic topology and form a natural domain for the global analysis of differential equations.

它们的整体性质用代数和代数拓扑的方法进行研究，并且形成微分方程式的整体分析的一个自然的领域。

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The integral matrix representation of the endomorphism monoid of a graph has been given by the method of the algebraic topology, some simple properties of the integral matrix semigroup have been discussed.

通过代数拓扑的方法，给出了图的自同态摹群的整矩阵表示，并讨论了整矩阵半群的简单性质。

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On the other hand, equivariant algebraic topology concerns the study of algebraic invariants of space with group actions. It is really a study of symmetries on spaces, and has always occupied a central role in mathematics.

在另一方面，等变代数拓扑关注于带有群作用的拓扑空间代数不变量的研究，其更深刻的本质在于对空间对称性的揭示，因此从来都在数学研究中占有重要的地位。

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Topology is traditionally decomposed into three parts: General topology, Algebraic topology and Differential topology.

习惯上拓扑学被分成点集拓扑、代数拓扑和微分拓扑三部分。

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A fracture network model based on algebraic topology theory has been developed to study fluid flow in the fracture dominant media.

提出一个基于代数拓扑理论的裂隙网络中流体分布的离散模型。

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Subsequently, the paper applies the theory of social system engineering and algebraic topology and brings forward a model of cluster analysis of relationships of NO.

接着，根据社会系统工程与拓扑代数的原理，提出了一个对网络关系进行评价与聚类的数学模型；

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To learn English Homeomorphic morphism and homotopy equivalence are two important concepts in the theory of algebraic topology.

同胚映射和同伦等价是代数拓扑学中的两个重要概念。

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In this paper, first, We give a topologically structural cluster analysis method by using algebraic topology.

本文首先利用代数拓扑学的思想，给出了拓扑结构聚类分析方法；

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Mobility is the life of the second rank market. In algebraic topology, J.

流动性是国债二级市场的生命力。在代数拓扑学中J。

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The Research Works of Professor S.D. Liao in Algebraic Topology

廖山涛教授的代数拓扑研究工作

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Eilenberg-MacLane space plays an essential role in Obstruction theory in Algebraic topology. And it is an important part of Homotopy theory.

Eilenberg-MacLane空间是代数拓扑中阻碍理论的核心，是同伦论的重要构成部分。

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The research of Wu includes the following fields: algebraic topology, algebraic geometry, game theory, history of mathematics, mathematics mechanization, and his most important contribution is to topology ( the Wu class and Wu formula), which is somewhat foundational in its field.

吴文俊的研究领域为拓扑学、代数几何、对策论、数学史、数学机械化，最重要的贡献是拓扑学（“吴示性类”、“吴公式”），在所属领域是基础性的。

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In 1945 MacLane and Eilenberg introduced the concept and theories of categories, which have played a role in many branches of mathematics such as algebraic geometry, topology, differential geometry and functional theories.

自从1945年MacLane与Eilenberg提出范畴的概念和理论以来，它在数学的许多分支，例如代数几何学、拓扑学、微分几何学以及函数理论中均已有所应用。

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