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The algebraic theory of torsion I. Foundations

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Algebraic and Geometric Topology

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1126))

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References

  1. H.Bass Algebraic K-theory Benjamin (1968)

    Google Scholar 

  2. , A. Heller and R.G. Swan The Whitehead group of a polynomial extension Publ. Math. I.H.E.S. 22, 61–79 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  3. F.T. Farrell The obstruction to fibering a manifold over a circle Indiana Univ. J. 21, 315–346 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  4. S. Ferry A simple-homotopy approach to the finiteness obstruction Springer Lecture Notes 870, 73–81 (1981)

    MathSciNet  MATH  Google Scholar 

  5. R.Fossum, H.-B.Foxby and B.Iversen The Whitehead torsion of a bounded complex and higher order Mennicke symbols preprint

    Google Scholar 

  6. D. Grayson (after D. Quillen) Higher algebraic K-theory II Springer Lecture Notes 551, 217–240 (1976)

    MathSciNet  Google Scholar 

  7. M. Karoubi Foncteurs dérivés et K-théorie ibid. 136, 107–186 (1970)

    MathSciNet  MATH  Google Scholar 

  8. W.Lück Eine allgemeine Beschreibung des Transfers für Faserungen auf projektiven Klassengruppen und Whiteheadgruppen Göttingen Ph.D. thesis (1984)

    Google Scholar 

  9. M. Mather Counting homotopy types of manifolds Topology 4, 93–94 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  10. J.P. May E ∞ -spaces, group completions and permutative categories L.M.S. Lecture Notes 11, 61–94 (1974)

    MathSciNet  MATH  Google Scholar 

  11. J. Milnor Whitehead torsion Bull. A.M.S. 72, 358–426 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  12. E.K. Pedersen On the K −i (-) functors J. of Algebra 90, 461–475 (1984)

    Article  MATH  Google Scholar 

  13. K −i -invariants of chain complexes Springer Lecture Notes 1060, 174–186 (1984)

    MathSciNet  Google Scholar 

  14. and A.A. Ranicki Projective surgery theory Topology 19, 239–254 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  15. and C.Weibel A nonconnective delooping of algebraic K-theory these proceedings

    Google Scholar 

  16. A.A. Ranicki Algebraic L-theory II: Laurent extensions Proc. L.M.S. (3) 27, 126–158 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  17. The algebraic theory of surgery ibid. 40, 87–283 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  18. The algebraic theory of finiteness obstruction Math. Scand. (to appear)

    Google Scholar 

  19. J. Shaneson Wall's surgery obstruction groups for G × ZZ Ann. of Maths. 90, 296–334 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  20. L. Siebenmann A total Whitehead torsion obstruction to fibering over the circle Comm. Math. Helv. 45, 1–48 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  21. R.G.Swan Algebraic K-theory Springer Lecture Notes 76 (1968)

    Google Scholar 

  22. C.T.C. Wall Foundations of algebraic L-theory ibid. 343, 266–300 (1973)

    MathSciNet  MATH  Google Scholar 

  23. C. Weibel K-theory of Azumaya algebras Proc. A.M.S. 81, 1–7 (1981)

    MathSciNet  MATH  Google Scholar 

  24. J.H.C. Whitehead Simple homotopy types Am. J. Math. 72, 1–57 (1950)

    Article  MathSciNet  MATH  Google Scholar 

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Andrew Ranicki Norman Levitt Frank Quinn

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© 1985 Springer-Verlag

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Ranicki, A. (1985). The algebraic theory of torsion I. Foundations. In: Ranicki, A., Levitt, N., Quinn, F. (eds) Algebraic and Geometric Topology. Lecture Notes in Mathematics, vol 1126. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0074445

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  • DOI: https://doi.org/10.1007/BFb0074445

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  • Print ISBN: 978-3-540-15235-4

  • Online ISBN: 978-3-540-39413-6

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