Open AccessTHE THEORY OF HOMOTOPY GROUP WITH MULTIPLE BASE POINTS
Author(s) -
Bz Li,
Fei Yan
Publication year - 1988
Publication title -
wuli xuebao
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.199
H-Index - 47
ISSN - 1000-3290
DOI - 10.7498/aps.37.128
Subject(s) - homotopy , base (topology) , homotopy group , group (periodic table) , mathematics , order (exchange) , whitehead theorem , combinatorics , n connected , pure mathematics , physics , mathematical analysis , quantum mechanics , finance , economics
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.