homotopy theory

Study of the Problems of Homotopy Theory in Category of Morphisms

态范畴的同伦论问题研究

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。

Application of Homotopy Theory in Defects of Liquid Crystals

同伦群理论在液晶缺陷中的应用

The topological structure of the superfluid He system has been studied using the homotopy theory for defects in ordered media developed in the 80s .

本文利用有序介质缺陷的同伦论系统地研究超流He系统的拓扑结构。

Homotopy Theory for Locales

Locale同伦理论

As the corresponding theoretical basis we restate the concerned results in homotopy theory as a theorem and call it the invariance theorem for homotopy equivalence transformation .

为此，我们将同伦理论中的有关结果整理成同伦等价变换不变性定理，以作为这方面的理论基础。

The most important content in Homotopy theory is to calculate the homotopy group of a topological space . Now the most useful method to calculate homotopy group is spectral sequence .

同伦论的重要内容就是计算空间的同伦群，目前计算同伦群的最重要方法是谱序列。

Cohomology operation belongs to Homotopy theory and can be used to calculate the homotopy group of topological space . Further more it has a bijection relationship with the cohomology group of the corresponding Eilenberg-MacLane space .

上同调算子也是同伦论的一部分重要内容，可以用来计算空间的同伦群，并且与相应的Eilenberg-MacLane空间的上同调群存在双射。

With regard to Schwarz lemma , Basing on the argument principle and homotopy theory , the author extend the classical Schwarz lemma from analytic function to meromorphic function whose number of the zeros are k th , and these functions are defined on the unit disk .

在Schwarz引理方面，基于辐角原理和同伦理论，作者将经典的Schwarz引理从单位圆盘上的解析函数推广到了具有k阶零点的亚纯函数。

In addition , the approximate calculation for Elastic Layered System ( ELS ) to be based on the homotopy neural network theory is discussed with the combination of major contents in the dissertation and the current development trend of ANN theory .

另外，结合本文的主要研究内容，以及当前神经网络理论发展的趋势，本文还探讨了基于同伦神经网络理论的弹性层状体系的近似计算。

Finally , a simple introduce of homotopy is employed . The classification of the static magnetic domain wall structures of tube - and envelope-type is made in an unified way using the homotopy theory .

并且简单介绍了拓扑学中同伦论的历史和思想，为后面提出新的解析方法进行理论上的铺垫。本文从拓扑学角度，对管状磁畴壁和闭合磁畴壁静态结构的分类问题，做了统一处理。