应用拓扑空间(组)的同伦等价变换于有序介质状态和缺陷的拓扑分类

Applying the Homotopy Equivalence Transformation of Topological Space Sets to the Topological Classification of States and Defects in Ordered Media

该文论述了拓扑空间(组)的同伦等价变换在有序介质状态和缺陷的拓扑分类中的应用问题.首先,我们指出,为使此分类获得简化并把所得到的绝对和相对同伦类集合构造成群,该变换是不可少的;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.其次,为使此定理的应用变得直接简便,我们还给出了关于拓扑空间(组)之间同伦等价的几个命题.最后,应用上述定理与命题,较系统地讨论了状态和缺陷的拓扑分类,其结果被概括成定理1～8.

In this paper the application of homotopy equivalence transformation of topological space sets to the topological classification of states and defects in ordered media is discussed.Firstly,an argument is presented about that for simplifying the classification procedure and constructing the absolute and relative homotopy class sets into groups, it is necessary to utilize the above-mentioned transformation.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.Secondly,in order to favor utilizing this theorem,several propositions are given on the homotopy equivalence between two topological space sets.Finally,the problem of absolute and relative topological classification of states and defects in ordered media is systematically studied ,the main results obtained are embodied in theorems 1～8.