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Finite domination and Novikov homology over strongly ℤ-graded rings

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Abstract

Let L be a unital Z-graded ring, and let C be a bounded chain complex of finitely generated L-modules. We give a homological characterisation of when C is homotopy equivalent to a bounded complex of finitely generated projective L 0-modules, generalising known results for twisted Laurent polynomial rings. The crucial hypothesis is that L is a strongly graded ring.

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References

  1. N. Bourbaki, Algebra I. Chapters 1–3, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 1998. Translated from the French. Reprint of the 1989 English translation.

    MATH  Google Scholar 

  2. E. C. Dade, Group-graded rings and modules, Math. Z. 174 (1980), 241–262.

    Article  MathSciNet  MATH  Google Scholar 

  3. J. A. Hillman and D. H. Kochloukova, Finiteness conditions and PDr-group covers of PDn-complexes, Math. Z. 256 (2007), 45–56.

    Article  MathSciNet  MATH  Google Scholar 

  4. T. Hüttemann, Double complexes and vanishing of Novikov cohomology, Serdica Math. J. 37 (2012), 295–304.

    MathSciNet  MATH  Google Scholar 

  5. T. Hüttemann, Vector bundles on the projective line and finite domination of chain complexes, Math. Proc. R. Ir. Acad. 115A (2015), Art. 2, 12.

    Google Scholar 

  6. A. Ranicki, The algebraic theory of finiteness obstruction, Math. Scand. 57 (1985), 105–126.

    Article  MathSciNet  MATH  Google Scholar 

  7. A. Ranicki, Finite domination and Novikov rings, Topology 34 (1995), 619–632.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Mathematical Sciences Research Centre, School of Mathematics and Physics, Queen’s University Belfast, Belfast, Northern Ireland, BT7 1NN, UK

    Thomas Hüttemann & Luke Steers

Authors
  1. Thomas Hüttemann
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  2. Luke Steers
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Correspondence to Thomas Hüttemann.

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Hüttemann, T., Steers, L. Finite domination and Novikov homology over strongly ℤ-graded rings. Isr. J. Math. 221, 661–685 (2017). https://doi.org/10.1007/s11856-017-1569-9

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  • DOI: https://doi.org/10.1007/s11856-017-1569-9

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