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arXiv · 1211.4994

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

Thomas Huettemann·David Quinn
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Abstract

Let C be a bounded cochain complex of finitely generated free modules over the Laurent polynomial ring L = R[x,1/x,y,1/y]. 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 characterises 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 obtained by tensoring C over L with R[[x,y]][1/xy] and R[x,1/x][[y]][1/y], and their variants obtained by swapping x and y, and replacing either indeterminate by its inverse.

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Thomas Huettemann, David Quinn. 2012-11-21. Finite domination and Novikov rings. Laurent polynomial rings in two variables. https://doi.org/10.1142/s0219498815500553

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