关于 3D和2D型SPin态的拓扑分类的注记

对铁磁体中的Ｓｐｉｎ态进行拓扑分类在物理学上有重要意义。本文用代数拓扑学中的Ｍａｙｅｒ－Ｖｉｅｔｏｒｉｓ正合序列计算了一类空间区域Ω的第一、二个整系数上同调，从而对占据该区域的铁磁体的３Ｄ和２Ｄ型Ｓｐｉｎ态进行了拓扑分类，这里所论的铁磁体中含有若干环状和穿过其中的柱状空腔，而且环状空腔可以是互相缠绕的。最后还讨论了这类铁磁体中的矢量场和标量场的某些全局性质。

Note on Topological Classification of 3D and 2D Spin States

Because of the important significance of the topological classification of Spin states, the Mayer Vietoris exact sequences in algebraic topology have been used to calculate the cohomology groups H 1(D,Z) and H 2(D,Z) so that the topological classification of 3D and 2D Spin states is obtained in ferromagnets D,in which the annulus type cavities and cylinder type cavities lie in the general position. In addition, some global properties of the fields on a ferromagnet are discussed.