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On four dimensional surgery and applications

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Commentarii Mathematici Helvetici

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References

  1. Browder, W.,Surgery on simply-connected manifolds, to appear.

  2. —,Surgery and the theory of differentiable transformation groups, [Proceedings of the Conference on Transformation Groups, New Orleans, 1967; (Springer-Verlag, New York, 1968)].

    Google Scholar 

  3. Diffeomorphisms of 1-connected manifolds, Trans. Amer. Math. Soc.128 (1967), 155–163.

    Article  MATH  MathSciNet  Google Scholar 

  4. Browder, W. andLevine, J.,Fibering manifolds over S 1, Comment. Math. Helv.40 (1965), 153–160.

    Article  MathSciNet  Google Scholar 

  5. Cappell, S., to appear.

  6. Farrell, F. T.,The obstruction to fibering a manifold over a circle, to appear. (See also Bull. Amer. Math. Soc.73 (1967), 734–740).

    Google Scholar 

  7. Farrell, F. T. andHsiang, W.-C., Manifolds with π1=Z xα G, to appear. (See also Bull. A.M.S.74 (1968), 548–553.)

    Article  MATH  MathSciNet  Google Scholar 

  8. Hsiang, W.-C. andShaneson, J. L.,Fake tori, (Proceedings of the Athens, Georgia conference on Topology of Manifolds, 1969,Markham Press, Chicago, 1970, 19–50). (See also Proc. Nat. Acad. Sci. U.S.A62 (1969), 687–691.)

    Google Scholar 

  9. Hudson, J. F. P.,Piecewise linear topology (Benjamin, New York, 1969).

    MATH  Google Scholar 

  10. Hirsh, M. W.,Immersions of manifolds, Trans. Amer. Math. Soc.93 (1959), 242–276.

    Article  MathSciNet  Google Scholar 

  11. Kervaire, M.,Geometric and algebraic intersection numbers, Comment. Math. Helv.39 (1965), 271–280.

    Article  MATH  MathSciNet  Google Scholar 

  12. Kervaire, M.,Le Théorème de Barden-Mazur-Stallings, Comment. Math. Helv.40 (1965), 31–42.

    Article  MATH  MathSciNet  Google Scholar 

  13. Kervaire, M. andMilnor, J.,On 2-spheres in 4-manifolds, Proc Nat. Acad. of Sci. U.S.A.47 (1961), 1651–7.

    Article  MATH  MathSciNet  Google Scholar 

  14. —,Groups of homotopy spheres: I, Ann. of Math.77 (1963), 504–537.

    Article  MathSciNet  Google Scholar 

  15. Kirby, R. andSiebenmann, L., to appear. (See also Bull. A.M.S.75 (1969), 742–9.)

    MATH  MathSciNet  Google Scholar 

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

    MATH  MathSciNet  Google Scholar 

  17. Lashof, R. andRothenberg, M.,Microbundles and smoothing, Topology3 (1965), 357–388.

    Article  MATH  MathSciNet  Google Scholar 

  18. Lashof, R. andShaneson, J.,Smoothing four-manifolds, Inv. Math. to appear.

  19. Lashof, R.,A procedure for killing the homotopy groups of differentiable manifolds [Proc. Amer. Math. Soc. Symp. in Pure Math III (Tuscon, 1961), pp. 39–55].

  20. Lashof R.,Lectures on the h-cobordism theorem, [Princeton University preliminary informal course notes, (Princeton University Press, 1965)].

  21. Lopez de Medrano, S.,Some results on involutions of homotopy spheres, [Proceedings of the conference on Transformation Groups, New Orleans, 1967; (Springer-Verlag, New York, 1968].

    Google Scholar 

  22. Novikov, S. P.,Homotopically equivalent manifolds: I, Amer. Math. Soc. Translations, series 2, vol. 48, 271–396.

  23. Rohlin, V. A.,A new result in the theory of 4-dimensional manifolds, Doklady8 (1952), 221–224.

    MathSciNet  Google Scholar 

  24. Shaneson, J. L.,Wall's surgery obstruction groups for Z×G, Ann. of Math.90 (1969), 296–334.

    Article  MathSciNet  Google Scholar 

  25. —,Non-simply-connected surgery and some results in low dimensional topology, Comment. Math. Helv.45 (1970), 333–352.

    MATH  MathSciNet  Google Scholar 

  26. —,On some non-simply-connected manifolds, [Proc. Amer. Math. Soc. Symposia in Pure Math., Vol. XXII, Algebraic Topology (1971), 221–229.]

    MathSciNet  Google Scholar 

  27. Sullivan, D.,Triangulating and smoothing homotopy equivalences, [mimeographed notes, (Princeton Univ, 1967)].

  28. Stallings, J.,On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology (a symposium in honor of M. Morse), (Princeton Univ. Press, 1965), pp. 245–254.

  29. Seifert, H. andThrellfall, W.,Lehrbuch der Topologie, (Teubner, Leipzig, 1934).

    Google Scholar 

  30. Wall, C. T. C.,Diffeomorphisms of 4-manifolds, Proc. Lond. Math. Soc.39 (1965), 131–140.

    Google Scholar 

  31. —,Diffeomorphisms of 4-manifolds, Proc. Lond. Math. Soc.84 (1966), 217–276.

    MathSciNet  Google Scholar 

  32. —,Surgery on compact manifolds, (Academic Press, London, 1970).

    MATH  Google Scholar 

  33. —,Free piecewise linear involutions on spheres, Bull. A.M.S.74 (1968), 553–8.

    Google Scholar 

  34. —,Poincaré Complexes: I, Ann. of Math.86 (1967), 213–245.

    Article  MathSciNet  Google Scholar 

  35. Whitney, H.,Differentiable manifolds, Ann. of Math.37 (1936), 645–680.

    Article  MathSciNet  Google Scholar 

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Both authors were partially supported by an NSF Grant.

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Cappell, S.E., Shaneson, J.L. On four dimensional surgery and applications. Commentarii Mathematici Helvetici 46, 500–528 (1971). https://doi.org/10.1007/BF02566862

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