On the odd primary cohomology of higher projective planes

Mark Foskey and Michael David Slack

Vol. 173 (1996), No. 1, 77–92

DOI: 10.2140/pjm.1996.173.77

Abstract

Let X be an n-fold loop space. Working with an auxiliary space P_pⁿX analogous to the projective plane P₂X, we show that the existence of certain Steenrod connections in H^∗(P_pⁿX;F_p) (p odd) implies the vanishing of certain corresponding Dyer-Lashof operations in H^∗(X;F_p), and vice versa.

Mathematical Subject Classification 2000

Primary: 55P35

Secondary: 55P47, 55S10, 55S12

Milestones

Received: 27 September 1993

Published: 1 March 1996