TOPOLOGICAL CLASSIFICATION OF 3D AND 2D SPIN STATES IN THE FERROMAGNETS CONTAINING ANNULUS- AND CYLINDER-TYPE CAVITIES

Methods of algebraic topology have been employed to classify ordinary (3D) and planar (2D) spin states in the ferromagnets containing annulus- and cylinder-type cavities. The main result of this paper is that the sets of homotopy classes of 3D and 2D spin states in a ferromagnet containing m non-winding up annulus-type cavities threaded by k cylinder-type cavities can be constructed into groups isomorphic to Z^m and Z^m+k, respectively. Here m,k = 0, 1, 2,…,Z^l denotes the l-dimensional discrete vector group.