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Surgery, BPL, BTOP and the PL bordism rings

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Part of the Lecture Notes in Mathematics book series (LNM,volume 249)

Keywords

  • Spectral Sequence
  • Homotopy Class
  • Surgery Problem
  • Adams Spectral Sequence
  • Serre Spectral Sequence

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Bibliography

  1. Anderson, P., "Cobordism classes of squares of orientable manifolds," Ann. of Math. 83, 47–53 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Araki, S., and Kudo, T., "Topology of Hn-spaces and H-squaring operations," Mem. Fac. Sci. Kyushu Univ. Ser. A 10, 85–120 (1956).

    MathSciNet  MATH  Google Scholar 

  3. Braun, H., "Geschlecter quadratischer formen," J. Reine Angew. Math. 182, 32–49 (1940).

    MathSciNet  MATH  Google Scholar 

  4. Browder, W., "The Kervaire invariant of framed manifolds," Ann. of Math. 90, 157–186 (1969).

    CrossRef  MathSciNet  MATH  Google Scholar 

  5. _____, "Surgery on simply connected manifolds," mimeographed notes, Princeton Univ. (1969).

    Google Scholar 

  6. _____, Liulevicius, A., and Peterson, F., "Cobordism theories," Ann. of Math. 84, 91–101 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Brown, E., "The Kervaire invariant of a manifold," Proc. Amer. Math. Soc. Summer Colloquium, Madison (1970).

    Google Scholar 

  8. Conner, P., and Floyd, E., Differentiable Periodic Maps. Springer, New York,1961.

    MATH  Google Scholar 

  9. Dyer, E., and Lashof, R., "Homology of iterated loop spaces," Amer. J. Math. 84, 35–88 (1962).

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. Gitler, S., and Stasheff, J., "The first exotic class of BF," Topology 4, 257–266 (1965).

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. Hirsch, M., and Mazur, B., "Smoothing theory," mimeographed notes, Cambridge Univ. (1964).

    Google Scholar 

  12. Kervaire, M., and Milnor, J., "Bernoulli numbers, homotopy groups and a theorem of Rohlin," Proc. Internat. Congress of Math., Edinburgh (1958).

    Google Scholar 

  13. _____, "Groups of homotopy spheres I," Ann. of Math. 77, 504–537 (1963).

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. Kirby, R., and Siebenmann, L. (to appear).

    Google Scholar 

  15. Kristensen, L., "On the cohomology of 2-stage Postnikov systems," Acta Math. 107, 73–123 (1962).

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Lashof, R., and Rothenberg, M. (to appear).

    Google Scholar 

  17. Mahowald, M., private communication.

    Google Scholar 

  18. Milgram, R. J., "Iterated loop spaces," Ann. of Math. 84, 386–403 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  19. _____, "The mod 2 spherical characteristic classes," Ann. of Math. 92, 238–261 (1970).

    CrossRef  MathSciNet  MATH  Google Scholar 

  20. _____, "Group representations and the Adams spectral sequence," Pacific J. Math. (to appear).

    Google Scholar 

  21. _____, "Unstable homotopy theory from the stable point of view," mimeographed notes, Princeton Univ. (1970).

    Google Scholar 

  22. _____, "Symmetries and operations in homotopy theory," Proc. Amer. Math. Soc. Summer Colloquium, Madison (1970).

    Google Scholar 

  23. _____, "Problems presented to the 1970 Amer. Math. Soc. colloquium in algebraic topology."

    Google Scholar 

  24. Milnor, J., "Microbundles," Topology 3, 53–80 (1964).

    CrossRef  MathSciNet  MATH  Google Scholar 

  25. Sullivan, "Triangulating homotopy equivalences," thesis, Princeton Univ. (1965).

    Google Scholar 

  26. Thom, R., "Quelques propriétés globales des variétés differentiables," Comment. Math. Helv. 28, 17–86 (1954).

    CrossRef  MathSciNet  MATH  Google Scholar 

  27. Tsuchiya, A., "Characteristic classes for PL microbundles," Trans. Amer. Math. Soc. (to appear).

    Google Scholar 

  28. Wall, C. T. C., "Surgery on non-simply connected manifolds," Ann. of Math. 84, 217–276 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

  29. _____, "Determination of the cobordism ring," Ann. of Math. 72, 292–311 (1960).

    CrossRef  MathSciNet  MATH  Google Scholar 

  30. Williamson, J., "Cobordism of combinatorial manifolds," Ann. of Math. 83, 1–33 (1966).

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1971 Springer-Verlag

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Milgram, R.J. (1971). Surgery, BPL, BTOP and the PL bordism rings. In: Hilton, P.J. (eds) Symposium on Algebraic Topology. Lecture Notes in Mathematics, vol 249. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0060896

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  • DOI: https://doi.org/10.1007/BFb0060896

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-05715-4

  • Online ISBN: 978-3-540-37082-6

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