Abstract
In this paper we determine the group \mathscr{E}(X ∨ Y) of pointed homotopy selfequivalence classes as the quotient of an iterated semi-direct product involving \mathscr{E}(X), \mathscr{E}(Y) and the 2n-th homotopy groups of X and Y, in the case where X and Y are (n−1)-connected 2n-manifolds or, more generally, are CW-complexes obtained by attaching a 2n-cell to a one-point union ∨mSn of m copies of the n-sphere for which a certain quadratic form has non-zero determinant (n≥3). In the case of manifolds this determinant is ±1. We include some examples, in particular one in which \mathscr{E}(X ∨ Y) does not itself inherit a semi-direct product structure.
