On the realization of homology classes by submanifolds
Haruo Suzuki · Transactions of the American Mathematical Society · 1958
Introduction.In [l] R. Thorn defines when a cohomology class in a manifold is realizable for a closed subgroup of an orthogonal group.He also defines when a homology class is realizable by a submanifold.He then shows the following.Let m be the dimension of a compact orientable differentiable manifold M. Any cohomology class of dimension 1,2, w -6, m -5, • • • , m is realizable for the orthogonal group 0(1) = 1, 0(2), 0(m-6), 0(m-5), ■ ■ ■ , 0(m) respectively.If a class z(E.Hm-k(M; Z) can be realized by a submanifold, then the cohomology class u^Hk(M; Z) which is dual to z satisfies 2r(p-l)+l