Abstract Suppose C is a bounded chain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,x -1]. Then C is R-finitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective R-modules if and only if the two chain complexes C - L R((x)) and C-L R((x-1)) are acyclic, as has been proved by Ranicki (Ranicki, Finite domination and Novikov rings, Topology 34(3) (1995), 619-632). Here R((x))=R[[x]][x -1] and R((x -1)) = R[[x -1]][x] are rings of the formal Laurent series, also known as Novikov rings. In this paper, we prove a generalisation of this criterion which allows us to detect finite domination of bounded below chain complexes of projective modules over Laurent rings in several indeterminates.
|Number of pages||16|
|Journal||Glasgow Mathematical Journal|
|Early online date||2 Aug 2012|
|Publication status||Published - Jan 2013|
- 2000 Mathematics Subject Classification Primary 55U15
- Secondary 18G35