Skip to main content
Log in

Non-simply-connected surgery and some results in low dimensional topology

  • Published:
Commentarii Mathematici Helvetici

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Barden, D.,Simply-connected five-manifolds, Ann. of Math.82 (1965), 365–385.

    Article  MathSciNet  Google Scholar 

  2. Blakers, A. L. andMassey, W. S.,The homotopy groups of a triad, I, II, III, Ann. of Math.53 (1951), 161–205;55 (1952), 192–201;58 (1953), 409–417.

    Article  MathSciNet  Google Scholar 

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

  4. Browder, W.,Cap products and Poincaré duality, mimeographed notes, Cambridge University, 1964,

  5. Browder, W.,Homotopy type of differentiable manifolds, Colloquium on Algebraic Topology, Aarhus 1962, 42–46.

  6. Browder, W.,The Kervaire invariant and its generalizations, Ann. of Math.90 (1969).

  7. — andLevine, J.,Fibering manifolds over a circle, Comment. Math. Helv.40 (1966), 153–160.

    Article  MATH  MathSciNet  Google Scholar 

  8. Cerf, J.,La nullité de π0 (DiffS 3), Sem. H. Cartan, 1962/3, Nos. 9, 10, 20, 21.

  9. Farrell, F. T.,The obstsruction to fibering a manifold over a circle, to appear. (See also Bull. Amer. Math. Soc.73 (1967), 741–4.)

    MATH  MathSciNet  Google Scholar 

  10. Farrell, F. T., andHsiang, W. C.,Manifolds with π1=ℤ ×αG, to appear. (See also Bull. Amer. Math. Soc.74 (1968), 548–553).

    MATH  MathSciNet  Google Scholar 

  11. Hirzebruch, F.,New Topological Methods in Algebraic Geometry, 3rd edition (Springer, N.Y. 1966).

    Google Scholar 

  12. Hsiang, W. C. andShaneson, J. L.,Fake tori, Proceedings of the Georgia Conference on Topology of Manifolds, 1969, to appear.

  13. Hu, S. T.,Homotopy theory (Academic Press, New York 1959).

    MATH  Google Scholar 

  14. Kato, M.,A concordance classification of P. L. homeomorphisms of S p×Sq, to appear.

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

    Article  MATH  MathSciNet  Google Scholar 

  16. — andMilnor, J.,On 2-spheres in 4-manifolds, Proc. Nat. Acad. Sci. USA47 (1961), 165–7.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  19. — andShaneson, J. L.,Classification of knots in codimension two, Bull. Amer. Math. Soc.75, (1969), 171–5.

    MATH  MathSciNet  Google Scholar 

  20. Milnor, J.,Lectures on Characteristic Classes, Princeton University mimeographed notes, 1957.

  21. —,Lectures on the h-cobordism theorem, Princeton Univ. Press, Princeton, New Jersey 1965.

    MATH  Google Scholar 

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

  23. Olum, P.,Non-abelian cohomology and Van Kampen's theorem, Ann. of Math.68 (1958), 658–668.

    Article  MathSciNet  Google Scholar 

  24. Pontrjagin, L. S.,Smooth manifolds and their applications in homotopy theory, Amer. Math. Soc. Translations, series 2, vol. 11, 1959.

  25. Serre, J.-P.,Homologie singulière des espaces fibrés, Ann. of Math.54 (1951), 425–505.

    Article  MathSciNet  Google Scholar 

  26. —,Groupes d'homotopie et classes des groupes abelians, Ann. of Math.58 (1953), 258–294.

    Article  MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  28. —,Wall's surgery obstruction groups for Z×G, suitable G, Bull. Amer. Math. Soc.74 (1968), 467–471.

    MATH  MathSciNet  Google Scholar 

  29. —,Embeddings of spheres in spheres with codimension two and h-cobordisms of S 1×S3, Bull. Amer. Math. Soc.74 (1968), 972–4.

    MATH  MathSciNet  Google Scholar 

  30. Spanier, E. H.,Algebraic Topology (McGraw-Hill, New York 1966).

    MATH  Google Scholar 

  31. Spivak, M.,Spaces satisfying Poincaré duality, Topology6 (1967), 77–102.

    Article  MATH  MathSciNet  Google Scholar 

  32. Steenrod, N.,The topology of fibre bundles, Princeton Mathematical Series, Princeton University Press, 1951.

  33. Sullivan, D.,Geometric Topology Seminar notes, Princeton Univ., 1967. (See also Bull. A.M.S.73 (1967), 598–600.)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  35. Wall, C. T. C.,On simply-connected 4-manifolds, J. London Math. Soc.39 (1965), 141–149.

    MathSciNet  Google Scholar 

  36. —,Diffeomorphisms of 4-manifolds, Proc. London Math. Soc.39 (1965), 131–140.

    Google Scholar 

  37. —,Surgery of non-simply-connected manifolds, Ann. of Math.84 (1966), 217–276.

    Article  MathSciNet  Google Scholar 

  38. Wall, C. T. C.,Surgery of compact manifolds, to appear.

  39. —,Poincaré complexes I, Ann. of Math.86, (1967), 213–245.

    Article  MathSciNet  Google Scholar 

  40. —,Finiteness conditions for CW complexes I, Ann. of Math.81 (1965), 56–69.

    Article  MathSciNet  Google Scholar 

Download references

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shaneson, J.L. Non-simply-connected surgery and some results in low dimensional topology. Commentarii Mathematici Helvetici 45, 333–352 (1970). https://doi.org/10.1007/BF02567336

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02567336

Keywords

Navigation