Abstract： A theorem is established that if the topoiogical space V is simply connected, the set of homotopy classes for the Sn→V continuous maps with N(≥1) base points, πn (V; v1, v2,…, vN), can be constructed into group isomorphic to the homotopy group of order n with single base point, πn(V) (referred to as the homotopy group of order n with N base points). Here, the condition that V is simply connected could not in general be neglected. Some corollaries are given. The application of this theorem and its corollaries to the topoiogical classification of magnetization states in ferromagnet is briefly- described with a few examples.
李伯臧,阎凤利. 多基点同伦群理论. 物理学报, 1988, 37(1): 131.
Cite this article:
LI BO-ZANG,YAN FENG-LI. THE THEORY OF HOMOTOPY GROUP WITH MULTIPLE BASE POINTS. Acta Phys. Sin., 1988, 37(1): 128-131.