Vol. 77, No. 2, 1978

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A vanishing theorem for the mod p Massey-Peterson spectral sequence

Masamitsu Mori

Vol. 77 (1978), No. 2, 473–481

A vanishing theorem and periodicity theorem for the classical mod 2 Adams spectral sequence were originally proved by Adams [1]. The results were extended to the unstable range by Bousfield [2]. The purpose of this paper is to show the analogue of Bousfield’s work for the mod p unstable Adams spectral sequence of Massey-Peterson type (called the mod p Massey-Peterson spectral sequence), where p is an odd prime. The results generalized those obtained by Liulevicius [5], [6] to the unstable range. As an immediate topological application we have the estimation of the upper bounds of the orders of elements in the p-primary component of the homotopy groups of, for example, an odd dimensional sphere, Stiefel manifold, or H-space.

Mathematical Subject Classification 2000
Primary: 55Q52
Secondary: 55S10
Received: 30 January 1977
Published: 1 August 1978
Masamitsu Mori