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.

Fleuve glauque : les départements de la Seine, banlieue des romans « Spécial Police » de Frédéric Dard

This paper studies the representation of suburbs as a place of anguish in the “Special Police” novels (Fleuve Noir publisher, Paris) by Frédéric Dard. This anxiety, it is argued, is what lends this collection of 25 novels some of their essential qualities, their unhealthy climate and absolute darkness. Dard’s suburbs fit into the traditions of realism; but the atmosphere, characters and plots owe to the American hardboiled school and like in film noir, space is stylized and dramatized, and often used to express a judgment of moral nature. Spatial representations in these novels are part of a critique of civilization and constitute a comment on the social modernization and public intervention in the development of the French territory in the postwar period. The novels written by Frédéric Dard from the mid-1950s to mid-1960s offer a profoundly original representation of suburban angst and what was not yet known at the time as the suburban malaise. Avoiding clichés and excessively connoted referential spaces, Dard anchor these noir novels he called “novels of the night” in landscapes that are both biographical and intertextual. The West Suburbs of Paris and what was
to become the Yvelines department are at the centre of Dard’s novelistic geography, turning into a mythical and deadly space in which is negotiated an acculturation in France of the evil and ruined world described in American noir.

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.