Skip to main content

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

The Functor K2 of Milnor

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

Keywords

  • Chain Complex
  • Geometric Interpretation
  • Closed Manifold
  • Grothendieck Group
  • Homology Sphere

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   54.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   69.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  MATH  Google Scholar 

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

    CrossRef  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.

    CrossRef  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.

    CrossRef  MathSciNet  Google Scholar 

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

    CrossRef  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 1973 Springer-Verlag

About this paper

Cite this paper

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

Download citation

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

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-06435-0

  • Online ISBN: 978-3-540-37770-2

  • eBook Packages: Springer Book Archive