Poincaré Complex Diagonals and the Bass trace Conjecture

Abstract

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.

Final prepublication version. This paper is to appear in, "Manifolds and K-Theory: in honour of Andrew Ranicki of the journal Proceedings of the Royal Society of Edinburgh Section A: Mathematics."

References in corpus (2)

• Homotopy idempotents on manifolds and Bass' conjectures
• On Finite domination and Poincaré duality