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多基点同伦群理论

李伯臧 阎凤利

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多基点同伦群理论

李伯臧, 阎凤利

THE THEORY OF HOMOTOPY GROUP WITH MULTIPLE BASE POINTS

LI BO-ZANG, YAN FENG-LI
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  • 本文建立了一个定理:当拓扑空间V单连通时,N(≥1)基点n阶同伦类集合πn(V;v1,v2,…,vN)可被构造成同构于单基点n阶同伦群πn(V)的群,叫做N基点n阶同伦群;并且V的单连通性一般是不可省略的条件。给出了一些推论。简要地触及了这个定理及其推论在铁磁状态拓扑分类中的应用问题。
    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.
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出版历程
  • 收稿日期:  1987-02-09
  • 刊出日期:  2005-07-04

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