Applying the homotopy equivalence transformation of topological space sets to the topological classification of states and defects in ordered media
Bo‐Zang Li, Yan Feng-Li · Acta Physica Sinica (Overseas Edition) · 1993
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 presented 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 classification of states and defects is systematically studied. The main results obtained are embodied in eight theorems.