CERTAIN SELF-HOMOTOPY EQUIVALENCES ON WEDGE PRODUCTS OF MOORE SPACES

Abstract

For a based 1-connected finite CW-complex X, let epsilon(X) denote the group of homotopy classes of self-homotopy equivalences on X, and epsilon(dim+r)(#) (X) the subgroup of epsilon(X) of homotopy classes of self-homotopy equivalences on X that induce the identity homomorphism on the homotopy groups of X in dimensions <= dim X + r. For two given Moore spaces M-1 = M(Z(q) , n + 1) and M-2 = M(Z(p) , n) with n >= 5, we investigate the subsets of [M-1; M-2] and [M-2; M-1] consisting of homotopy classes of maps that induce the trivial homomorphism between the homotopy groups of M-1 and those of M-2 in dimensions <= dim X + r. Using the results of this investigation, we completely determine the subgroups epsilon(dim+r)(#) (M(Z(q) , n + 1) v M(Z(p) , n) where p and q are positive integers, for n >= 5 and r = 0,1.