Le thème du mensonge dans Le Petit Canard de Jacques Laurent’

ADEFFI annual conference
Trinity College Dublin
October 2007

Finite domination and Novikov rings: Laurent polynomial rings in two variables

Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called R-finitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.

Finite domination and Novikov rings. Laurent polynomial rings in several variables

We present a homological characterisation of those chain complexes of modules over a Laurent polynomial ring in several indeterminates which are finitely dominated over the ground ring (that is, are a retract up to homotopy of a bounded complex of finitely generated free modules). The main tools, which we develop in the paper, are a non-standard totalisation construction for multi-complexes based on truncated products, and a high-dimensional mapping torus construction employing a theory of cubical diagrams that commute up to specified coherent homotopies.

Laurent [Marcel], Lapierre, Jouhaux (fils) [responsables syndicaux de la CGT] : [photographie de presse] / [Agence Rol]

Référence bibliographique : Rol, 59274

St Laurent-lès-Mâcon [le bateau Parisien 2 sur la Saône] : [photographie de presse] / [Agence Rol]

Référence bibliographique : Rol, 60536

M. Charles Laurent [nommé ambassadeur à Berlin] : [photographie de presse] / [Agence Rol]

Référence bibliographique : Rol, 60068