### 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 language | English |
---|---|

Article number | 1550055 |

Journal | Journal of Algebra and its Applications |

Volume | 14 |

Issue number | 4 |

Early online date | 9 Jan 2015 |

DOIs | |

Publication status | Published - 29 May 2015 |

### Keywords

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

## Fingerprint Dive into the research topics of 'Finite domination and Novikov rings: Laurent polynomial rings in two variables'. Together they form a unique fingerprint.

## Cite this

Hüttemann, T., & Quinn, D. (2015). 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