Poincaré Complex Diagonals and the Bass trace Conjecture

For a finitely dominated Poincaré duality space $M$, we show how the author’s total obstruction to the existence of a Poincaré embedding of the diagonal map $M\to M\times M$ relates to the Reidemeister trace of the identity map of $M$. We also show that if the dimension of $M$ is even and at least four, and if ${\pi }_1(M)$ is a finite direct product of cyclic groups of order two, then the diagonal map admits a Poincaré embedding.