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

Thomas Hüttemann; David Quinn

doi:10.1016/j.jpaa.2015.12.004

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

Thomas Hüttemann^*, David Quinn

^*Corresponding author for this work

Mathematical Science

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	2648-2682
Number of pages	35
Journal	Journal of Pure and Applied Algebra
Volume	220
Issue number	7
Early online date	12 Jan 2016
DOIs	https://doi.org/10.1016/j.jpaa.2015.12.004
Publication status	Published - Jul 2016

Keywords

18G35
55U15
Primary
secondary

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AB - 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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KW - secondary

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ER -

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

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Keywords

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