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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 Rfinitely dominated, i.e. homotopy equivalent over R to a bounded chain complex of finitely generated projective Rmodules 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 (A. 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.
Original language  English 

Pages (fromto)  145160 
Number of pages  16 
Journal  Glasgow Mathematical Journal 
Volume  55 
Issue number  1 
Early online date  02 Aug 2012 
DOIs  
Publication status  Published  Jan 2013 
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Dive into the research topics of 'Finite domination and Novikov rings. Iterative approach'. Together they form a unique fingerprint.Projects
 1 Active
Activities
 1 Invited or keynote talk at national or international conference

The algebraic theory of finite domination
Thomas Huettemann (Invited speaker)
21 Jan 2019Activity: Talk or presentation types › Invited or keynote talk at national or international conference
Research output
 2 Citations
 2 Article

Vector bundles on the projective line and finite domination of chain complexes
Huettemann, T., 2015, In: Mathematical Proceedings of the Royal Irish Academy. 115A, 1, 12 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile303 Downloads (Pure) 
Finite domination and Novikov rings: Laurent polynomial rings in two variables
Huttemann, T. & Quinn, D., May 2014, In: Journal of Algebra and its Applications. 14, 4, 44 p., 1550055.Research output: Contribution to journal › Article › peerreview
Open AccessFile2 Citations (Scopus)595 Downloads (Pure)