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Abstract
Let C be a bounded cochain complex of finitely generatedfree modules over the Laurent polynomial ring L = R[x, x−1, y, y−1].The complex C is called Rfinitely dominated if it is homotopy equivalentover R to a bounded complex of finitely generated projective Rmodules.Our main result characterises Rfinitely dominated complexesin terms of Novikov cohomology: C is Rfinitely dominated if andonly if eight complexes derived from C are acyclic; these complexes areC ⊗L R[[x, y]][(xy)−1] and C ⊗L R[x, x−1][[y]][y−1], and their variants obtainedby swapping x and y, and replacing either indeterminate by its inverse.
Original language  English 

Article number  1550055 
Number of pages  44 
Journal  Journal of Algebra and its Applications 
Volume  14 
Issue number  4 
DOIs  
Publication status  Published  May 2014 
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Dive into the research topics of 'Finite domination and Novikov rings: Laurent polynomial rings in two variables'. Together they form a unique fingerprint.Projects
 1 Active

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

Toric varieties, Novikov homology and finiteness conditions for chain complexes
Thomas Huettemann (Speaker) & Silvia Sabatini (Organiser)
11 Jul 2018Activity: Talk or presentation types › Oral presentation
Profiles

Thomas Huettemann
 School of Mathematics and Physics  Senior Lecturer
 Mathematical Sciences Research Centre
Person: Academic
Research output
 2 Citations
 3 Article

Finite domination and NOVIKOV homology over strongly Z^{2}graded rings
Hüttemann, T. & Steers, L., 28 Jul 2023, (Early online date) In: Proceedings of the Royal Society of Edinburgh. Section A. Mathematics. 33 p.Research output: Contribution to journal › Article › peerreview
Open AccessFile24 Downloads (Pure) 
Finite domination and Novikov rings. Iterative approach
Huettemann, T. & Quinn, D., Jan 2013, In: Glasgow Mathematical Journal. 55, 1, p. 145160 16 p.Research output: Contribution to journal › Article › peerreview
2 Citations (Scopus) 
Double complexes and vanishing of Novikov cohomology
Hüttemann, T., 01 Dec 2011, In: Serdica Mathematical Journal. 37, 4, p. 295304Research output: Contribution to journal › Article › peerreview
Open AccessFile