Geodesic
FINITE DOMINATION AND NOVIKOV RINGS. ITERATIVE APPROACH
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 145-160

Voir la notice de l'article provenant de la source Cambridge University Press

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 ⊗LR((x)) and C ⊗LR((x−1)) are acyclic, as has been proved by Ranicki (A. Ranicki, Finite domination and Novikov rings, Topology34(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.
DOI : 10.1017/S0017089512000419
Mots-clés : Primary 55U15, Secondary 18G35 
HÜTTEMANN, THOMAS; QUINN, DAVID. FINITE DOMINATION AND NOVIKOV RINGS. ITERATIVE APPROACH. Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 145-160. doi: 10.1017/S0017089512000419
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