DIMENSION DEFECTS AND THE HOPF INVARIANT

Abstract

The concept of dimension defect of a mapping was introduced by H. Hopf in 5]. We generalize and answer questions about mappings S³ → S² which he raised at the end of that paper. Our main result is that a mapping S^2n-1 → Sⁿ with non-vanishing Hopf invariant does not have dimension defect.