Let M(m) be a closed and oriented submanifold of a closed or oriented
manifold N-n, such that [M, i] = 0 is an element of Omega(m) (N), wher
e i: M --> N is the inclusion and Omega(m) (N) is the mth oriented bor
dism group of N. If n = m + 2 or m less than or equal to 3 or m less t
han or equal to 4 and n not equal 7 then M bounds in N.