Subject: response to Karoubi's question From: "FERNANDO MURO JIMENEZ" Date: Fri, 24 Sep 2004 19:23:53 +0200 To: Dear Max, As far as I know one of the latest works on Pontrjagin operations was Baues's attempt to generalize the Pontrjagin square to cohomology with local coefficients in an arbitrary module over the fundamental group. This is part of his book on 4-dimensional complexes (1991). There Baues defines obstructions to the existence of such a cohomology operation and makes some explicit computations by using his algebraic model for 3-types (quadratic modules, a Peiffer-nilpotent analogue of Conduche's 2-crossed modules). However this approach does not use cup-i-products, as Whitehead originally did. Best regards, Fernando. ______________________ Fernando Muro Dept. Geometría y Topología Facultad de Matemáticas Universidad de Sevilla Apdo.1160 - 41080 Sevilla SPAIN fmuro@us.es http://www.aloj.us.es/fmuro/