Finite domination and Novikov rings: Laurent polynomial rings in two variables

Thomas Hüttemann, David Quinn

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Abstract

Let C be a bounded cochain complex of finitely generated free 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 equivalent over R to a bounded complex of finitely generated projective R-modules. Our main result characterizes R-finitely dominated complexes in terms of Novikov cohomology: C is R-finitely dominated if and only if eight complexes derived from C are acyclic; these complexes are C - L Rx, y[(xy) -1] and C - L R[x, x-1]y[y-1], and their variants obtained by swapping x and y, and replacing either indeterminate by its inverse.

Original languageEnglish
Article number1550055
JournalJournal of Algebra and its Applications
Volume14
Issue number4
Early online date9 Jan 2015
DOIs
Publication statusPublished - 29 May 2015

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Keywords

  • algebraic mapping torus
  • Finite domination
  • multi-complex
  • Novikov homology
  • totalisation
  • truncated product

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Applied Mathematics

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