On six-connected finite H-spaces

James Peicheng Lin and Frank Williams

Vol. 156 (1992), No. 1, 185–199

DOI: 10.2140/pjm.1992.156.185

Abstract

In this note we shall prove the following theorem.

Main Theorem Let X be a 6-connected finite H-space with associative mod 2 homology. Further, suppose that Sq⁴H⁷(X;Z₂) = 0 and Sq¹⁵H¹⁵(X;Z₂) = 0. Then X is either contractible or has the homotopy type of a product of seven-spheres.

Mathematical Subject Classification 2000

Primary: 55P45

Secondary: 55R35, 55S05, 55S20

Milestones

Received: 18 January 1990

Revised: 30 October 1991

Published: 1 November 1992