中国物理B ›› 1993, Vol. 2 ›› Issue (5): 321-332.doi: 10.1088/1004-423X/2/5/001

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APPLYING THE HOMOTOPY EQUIVALENCE TRANSFORMATION OF TOPOLOGICAL SPACE SETS TO THE TOPOLOGICAL CLASSIFICATION OF STATES AND DEFECTS IN ORDERED MEDIA

阎凤利1, 李伯臧2   

  1. (1)Department of Physics, Hebei Normal University, Shijiazhang 050016,China; (2)Institute of Physics, Academia Sinica, Beijing 100080,China
  • 收稿日期:1992-08-06 出版日期:1993-05-20 发布日期:1993-05-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China.

APPLYING THE HOMOTOPY EQUIVALENCE TRANSFORMATION OF TOPOLOGICAL SPACE SETS TO THE TOPOLOGICAL CLASSIFICATION OF STATES AND DEFECTS IN ORDERED MEDIA

LI BO-ZANG (李伯臧)a, YAN FENG-LI (阎凤利)b   

  1. a Institute of Physics, Academia Sinica, Beijing 100080, China; b Department of Physics, Hebei Normal University, Shijiazhang 050016, China
  • Received:1992-08-06 Online:1993-05-20 Published:1993-05-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China.

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摘要： In this paper the application of homotopy equivalence transformation (HET) of topological space sets to the topological classification of states and defects in ordered media is discussed. Firstly, an argument is pres-ented about the idea that for simplifying and even working out the classification and constructing homotopy class sets into groups, it is crucial to utilize the HET. As the theoretical basis for doing this we sum up the relevant results in homotopy theory into a theorem, called the "invariance theorem for HET". Secondly, in order to favor the utilization of this theorem, several propositions on homotopy equivalence between space sets are given. Finally, the absolute and relative topological dassification of states and defects is systemtically studied. The main results obtained are embodied in eight theorems.

Abstract: In this paper the application of homotopy equivalence transformation (HET) of topological space sets to the topological classification of states and defects in ordered media is discussed. Firstly, an argument is pres-ented about the idea that for simplifying and even working out the classification and constructing homotopy class sets into groups, it is crucial to utilize the HET. As the theoretical basis for doing this we sum up the relevant results in homotopy theory into a theorem, called the "invariance theorem for HET". Secondly, in order to favor the utilization of this theorem, several propositions on homotopy equivalence between space sets are given. Finally, the absolute and relative topological dassification of states and defects is systemtically studied. The main results obtained are embodied in eight theorems.

中图分类号:  (Theories and models of crystal defects)

  • 61.72.Bb
61.72.J- (Point defects and defect clusters) 02.40.Re (Algebraic topology) 02.20.-a (Group theory)