### 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 language | English |
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Article number | 1550055 |

Number of pages | 44 |

Journal | Journal of Algebra and its Applications |

Volume | 14 |

Issue number | 4 |

DOIs | |

Publication status | Published - May 2014 |

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## Cite this

Huttemann, T., & Quinn, D. (2014). Finite domination and Novikov rings: Laurent polynomial rings in two variables.

*Journal of Algebra and its Applications*,*14*(4), [1550055]. https://doi.org/10.1142/S0219498815500553