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.
ASJC Scopus subject areas
- Algebra and Number Theory
Huettemann, T., & Quinn, D. (2016). Finite domination and Novikov rings. Laurent polynomial rings in several variables. Journal of Pure and Applied Algebra, 220(7), 2648-2682. https://doi.org/10.1016/j.jpaa.2015.12.004