Paper read at the Symposium on Categorical Algebra and Topology University of Cape Town 29 June—3 July 1981

TODA BRACKETS AND THE CATEGORY OF HOMOTOPY PAIRS

Published in: Quaestiones Mathematicae
Volume 6 , issue 1-3 , 1983 , pages: 107–128

DOI: 10.1080/16073606.1983.9632295

Author(s): KA Hardie Department of Mathematics, South Africa , AV Jansen Department of Mathematics, South Africa

Keywords: 55Q05 , 55Q10 , 55Q35

Abstract

A new treatment is given of the cylinder-web diagram and associated diagonal sequences in homotopy pair theory. The efficiency of the diagram as a machine for computing homotopy pair groups is enhanced by a result that traces the path of a Toda bracket element through the arrows of the diagram. The diagonal factorization problem for a homotopy pair class is studied and related to the behaviour of Toda brackets. A necessary and sufficient condition for the vanishing of a Toda bracket is obtained.

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