Abstract: In this paper the problem of topological classification of ordinary (3D) and planar(2D) spin states in a ferromagnet including an annular cavity is discussed. It is verified that the set of homotopy classes of either 3D or 2D spin states in such ordered medium can be constructed into the groups isomorphic to Z, the additive group of integers.

Key words: topological classification, spin states, ferromagnet, annular cavity