On the realizabilities of integral homology classes by orientable submanifolds
Yoshihiro Shikata · Osaka City University (Osaka City University) · 1961
The present paper is concerned with the problem: which integral homology class of a compact orientable differentiable manifold is realizable by a non-singularly imbedded submanifold? As was shown by Thom [5], this problem is reduced to the mapping problem of the manifold into the Thom complex MSO for the rotation group SO; he solved this problem for homology classes of dimensions ≤ 7 provided the dimension of manifold is less than 17....