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

Thomas Hüttemann*, David Quinn

*Corresponding author for this work

Research output: Contribution to journalArticle

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 languageEnglish
Pages (from-to)2648-2682
Number of pages35
JournalJournal of Pure and Applied Algebra
Volume220
Issue number7
Early online date12 Jan 2016
DOIs
Publication statusPublished - Jul 2016

Fingerprint

Laurent Polynomials
Several Variables
Polynomial ring
Domination
Ring
Module
Retract
Commute
Homotopy
Finitely Generated
Torus
High-dimensional
Diagram

Keywords

  • 18G35
  • 55U15
  • Primary
  • secondary

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Finite domination and Novikov rings. Laurent polynomial rings in several variables. / Hüttemann, Thomas; Quinn, David.

In: Journal of Pure and Applied Algebra, Vol. 220, No. 7, 07.2016, p. 2648-2682.

Research output: Contribution to journalArticle

Hüttemann, Thomas ; Quinn, David. / Finite domination and Novikov rings. Laurent polynomial rings in several variables. In: Journal of Pure and Applied Algebra. 2016 ; Vol. 220, No. 7. pp. 2648-2682.
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