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arXiv · 1410.4352

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

Thomas Huettemann·David Quinn
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Abstract

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.

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Thomas Huettemann, David Quinn. 2014-10-16. Finite domination and Novikov rings. Laurent polynomial rings in several variables. https://doi.org/10.1016/j.jpaa.2015.12.004

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