A theory of PWD-structures (Q880126)

A PWD (product-wedge diagonal) structure on a space \(X\) consists of a space \(D_nX\) and maps \(\rho: X \to D_nX\), \(\sigma: \vee_{i=1}^nX \to D_nX\), \(\tau: D_nX \to X^n\) such that \(\tau\sigma\) is homotopic to the inclusion \(\vee_{i=1}^nX \to X^n\) and \(\tau\rho: X \to X^n\) is homotopic to the diagonal. This structure generalizes some previosly known structures (Whitehead fat wedge, double mapping cylinder, etc.). The authors develop a general theory of PWD-structures. In particular, they obtain some results of Berstein--Hilton type.