Homotopy commutative obstructions for liftings

Abstract

In this paper we study the c 2 invariant originally introduced by Williams. In particular, it has been shown to be useful to know when the c 2 invariant of an H-map lands in the modules PH∗( X) ⊗ PH∗( X), for X a homotopy commutative H-space. New methods using projective planes are introduced and examples are given where the c 2-invariant does not lie in PH∗( X) ⊗ PH∗( X). This paper corrects an error in [J.P. Lin and F. Williams, Primitivity of the c 2 invariant, J. Pure Appl. Algebra 43 (1986) 289-298].