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Decomposition formula of laurent extension in algebraic K-theory and the role of codimension 1 submanifold in topology

  • The Functor K2 of Milnor
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“Classical” Algebraic K-Theory, and Connections with Arithmetic

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 342))

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References

  1. H. Bass: Algebraic K-theory, Benjamin (1968) New York.

    Google Scholar 

  2. H. Bass, A. Heller and R. Swan: The Whitehead group of a polynomial extension, Publ. I.H.E.S. No. 22 (1964) 61–70.

    Google Scholar 

  3. H. Bass and M.P. Murthy: Grothendieck group and Picard groups of abelian group rings, Ann. of Math. Vol. 86 (1967) 16–73.

    Article  MathSciNet  MATH  Google Scholar 

  4. E. Eilenberg and N. Steenrod: Foundations of Algebraic topology, Princeton Math. Series, Princeton Univ. Press, Princeton, N. J. 1952.

    MATH  Google Scholar 

  5. R. D. Edwards and R. Kirby: Deformations of spaces of imbeddings. Ann. of Math. Vol. 93 (1971) 63–88.

    Article  MathSciNet  MATH  Google Scholar 

  6. F. T. Farrell and W. C Hsiang: A Formula for K1Rα[T], Proc. of Sym. in Pure Math. AMS Vol. XVII (1970) 192–218.

    Article  MathSciNet  Google Scholar 

  7. F. T. Farrell and W. C. Hsiang: Manifold with π1=G xα T (to appear in Amer. J. Math.).

    Google Scholar 

  8. F. T. Farrell and W. C. Hsiang: H: cobordant manifolds are not necessarily homeomorphic, Bull.AMS vol. 73 (1967) 741–744.

    Article  MathSciNet  MATH  Google Scholar 

  9. S. Gersten: Thesis, Cambridge University, 1965.

    Google Scholar 

  10. S. Gersten: Homotopy theory of rings and algebraic K-theory, Bull.AMS Vol. 77 (1971) 117–119.

    Article  MathSciNet  MATH  Google Scholar 

  11. A. Hatcher and J. Wagoner: Pseudo-isotopies on non-simply connected manifolds and the functor K2. (To appear).

    Google Scholar 

  12. A. Hatcher: The second obstruction for pseudo-isotopies. (To appear).

    Google Scholar 

  13. J. W. Milnor: Introduction to algebraic K-theory, Ann. of Math. Studies, Princeton University Press 1971, Princeton, N. J.

    MATH  Google Scholar 

  14. J. W. Milnor: Whitehead torsion, Bull. AMS Vol. 72 (1966) 358–426.

    Article  MathSciNet  MATH  Google Scholar 

  15. J. Milnor: Two complexes which are homeomorphic but combinatorially distinct, Ann. of Math. Vol. 74 (1961) 575–590.

    Article  MathSciNet  MATH  Google Scholar 

  16. D. Quillen: The K-theory associated to a finite field, Ann. of Math. (To appear).

    Google Scholar 

  17. D. Quillen: (To appear).

    Google Scholar 

  18. L. Siebenmann: Torsion invariants for pseudo-isotopies on closed manifolds, Notices AMS Vol. 14 (1967) 942.

    Google Scholar 

  19. L. Siebenmann: A total Whitehead torsion obstruction to fibring over the circle. Comment. Math. Helv. Vol. 45 (1970) 1–48.

    Article  MathSciNet  MATH  Google Scholar 

  20. J. Stallings: On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology, (A Sym. in honor of M. Morse), Princeton Univ. Press, Princeton, N. J. 245–254.

    Google Scholar 

  21. J. Wagoner: On K2 of the Laurent polynomial ring, Amer. J. Math. Vol. 93 (1972) 123–138.

    Article  MathSciNet  Google Scholar 

  22. C. T. C. Wall: Finiteness conditions for CW-complexes, Ann. of Math. Vol. 81 (1965) 56–69.

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Fine Hall Princeton University, Princeton, N. J.

    Wu-chung Hsiang

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  1. Wu-chung Hsiang
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H. Bass

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© 1973 Springer-Verlag

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Hsiang, Wc. (1973). Decomposition formula of laurent extension in algebraic K-theory and the role of codimension 1 submanifold in topology. In: Bass, H. (eds) “Classical” Algebraic K-Theory, and Connections with Arithmetic. Lecture Notes in Mathematics, vol 342. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0073730

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  • DOI: https://doi.org/10.1007/BFb0073730

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06435-0

  • Online ISBN: 978-3-540-37770-2

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