Exact sequences in stable homotopy pair theory

Abstract

A cylinder-web diagram with associated diagonal sequences is described in stable homotopy pair theory. The diagram may be used to compute stable homotopy pair groups and also stable track groups of two-cell complexes. For the stable Hopf class η \eta the stable homotopy pair groups G k ( η , η ) ( k ⩽ 8 ) {G_k}(\eta ,\eta )(k \leqslant 8) are computed together with some of the additive structure of the stable homotopy ring of the complex projective plane.