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

Thomas Huttemann, David Quinn

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1 Citation (Scopus)
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Abstract

Let C be a bounded cochain complex of finitely generatedfree 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 equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises R-finitely dominated complexesin terms of Novikov cohomology: C is R-finitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.
Original languageEnglish
Article number1550055
Number of pages44
JournalJournal of Algebra and its Applications
Volume14
Issue number4
DOIs
Publication statusPublished - May 2014

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