Skip to main content
Log in

The relationship between homology and topological manifolds via homology transversality

  • Published:
Inventiones mathematicae Aims and scope

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. Brumfiel, G., Morgan, J.: Homotopy theoretic consequences of N. Levitt's obstruction theory to transversality for spherical fibrations, Pacific J. of Math.67, 1–100 (1976)

    Google Scholar 

  2. Galewski, G., Stern, R.: Geometric transversality and bordism theories. Preprint

  3. Kirby, R., Siebenmann, L.: On the triangulation of manifolds and the Hauptvermutung. Bull. Amer. Math Soc.75, 742–749 (1969)

    Google Scholar 

  4. Kirby, R., Siebenmann, L.: Essays on topological manifolds, smoothings and triangulations. Annals of mathematics Studies, No. 88, Princeton New Jersey: Princeton University Press 1977

    Google Scholar 

  5. Levitt, N.: Poincare' duality cobordism. Ann. of Math.96, 211–244 (1972)

    Google Scholar 

  6. Levitt, N., Morgan, J.: Transversality structures andPL structures on spherical fibrations. Bull. Amer. Math. Soc.78, 1064–1068 (1972)

    Google Scholar 

  7. Martin, N.: On the difference between homology and piecewise linear bundles. J. of London Math. Soc. (2)6, 197–204 (1973)

    Google Scholar 

  8. Martin, N.: Transverse regular maps of homology manifolds. Proc. Camb. Phil. Soc.74, 29–38 (1973)

    Google Scholar 

  9. Martin, N., Maunder, C.: Homology cobordism bundles. Topology10, 93–110 (1971)

    Google Scholar 

  10. Matumoto, T.: Variétés simpliciales d'homologie et variétés topologiques métrisables. Thesis, Univ. de Paris-Sud, 91405, Orsay, 1976

    Google Scholar 

  11. Matumoto, T., Matsumoto, Y.: The unstable difference between homology cobordism and piecewise linear block bundles. Tôhoku Math. J. (2)27, 57–68 (1975)

    Google Scholar 

  12. Maunder, C.: An H-cobordism theorem for homology manifolds. Proc. London Math. Soc. (3)25, 137–155 (1972)

    Google Scholar 

  13. McCrory, C.: Cone complexes andPL transversality. Trans. Amer. Math. Soc.207, 269–291 (1975)

    Google Scholar 

  14. Rourke, C., Sanderson, B.: Block bundles I. Ann. of Math. (2)87, 1–28 (1968)

    Google Scholar 

  15. Rourke, C., Sanderson, B.: On topological neighborhoods. Composito Math.22, 387–424 (1970)

    Google Scholar 

  16. Rourke, C., Sanderson, B.: δ-sets. II. Block bundles and block fibrations. Quart. J. of Math.22, 465–485 (1971)

    Google Scholar 

  17. Siebenmann, L.: Are non-triangulable manifolds triangulable? In Topology of Manifolds, J.C. Cantrell and C.H. Edwards, Jr., eds. Chicago, Ill.: Markham 1969

    Google Scholar 

  18. Wall, C.T.C.: Surgery on compact manifolds. London Math. Soc. Monograph No. 1. London-New York: Academic Press 1970

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Supported in part by National Science Foundation grant GP 29585-A 4

Supported in part by a Faculty Research grant at the University of Utah and by National Science Foundation grant MCS 76-06393

Rights and permissions

Reprints and permissions

About this article

Cite this article

Galewski, D.E., Stern, R.J. The relationship between homology and topological manifolds via homology transversality. Invent Math 39, 277–292 (1977). https://doi.org/10.1007/BF01402977

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01402977

Keywords

Navigation