Original Articles

DIMENSION DEFECTS AND THE HOPF INVARIANT

Published in: Quaestiones Mathematicae
Volume 5 , issue 3 , 1982 , pages: 305–315

DOI: 10.1080/16073606.1982.9632271

Author(s): H. SCHLAGBAUER Department of Mathematics, Republic of South Africa

Keywords: 55Q25 , 55M20 , 55F60

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.

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