HOMOTOPY COMMUTATIVE OBSTRUCTIONS FOR LIFTINGS

In this paper we study the c2 invariant originally introduced by Willi ams. In particular, it has been shown to be useful to know when the c2 invariant of an H-map lands in the modules PH(X) X PH*(X), for X a h omotopy commutative H-space. New methods using projective planes are i ntroduced and examples are given where the c2-invariant does not lie i n PH(X) X PH*(X). This paper corrects an error in [J. P. Lin and F. W illiams, Primitivity of the c2 invariant, J. Pure Appl. Algebra 43 (19 86) 289-2981.