Skip to main content
Log in

Idempotent comultiplications on graded algebras

  • Published:
Geometriae Dedicata Aims and scope Submit manuscript

Abstract

We classify all idempotent comultiplications on a graded anticommutative algebra up to degree 3, provided its components are torsion free, and topologically realize all algebraic possibilities. Then we extend some results to dimension n and obtain topological consequences about closed n-manifolds with cohomology of special type.

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.

Similar content being viewed by others

References

  1. Ayres, F., Matrices, McGraw-Hill, New York, 1962.

    Google Scholar 

  2. Coddington, E. A. and Levinson, N., Theory of Ordinary Differential Equations, McGraw-Hill, New York, Toronto, London, 1955.

    Google Scholar 

  3. Fomenko, A. T., Fuchs, D. B. and Gutenmacher, V. L., Homotopic Topology, Akadémiai Kiadó, Budapest, 1986.

    Google Scholar 

  4. Greub, W. H., Multilinear Algebra, Springer-Verlag, Berlin, Heidelberg, New York, 1967.

    Google Scholar 

  5. Hofmann, K. H. and Mostert, P. S., Cohomology Theories for Compact Abelian Groups, VEB Deutscher Verlag der Wissenschaften, Berlin, 1973.

    Google Scholar 

  6. Hofmann, K. H. and Strambach, K., ‘Idempotent multiplications on surfaces and aspherical spaces’, Rocky Mount. Math. J. (to appear).

  7. MacLane, S. and Birkhoff, G., A Survey on Modern Algebra, Macmillan Company, New York, 1965.

    Google Scholar 

  8. Madsen, I. and Milgram, R. J., ‘The classifying spaces for surgery and cobordism of manifolds’, Ann. Math. Studies 92, Princeton Univ. Press, Princeton, N.J., 1979.

    Google Scholar 

  9. Mandelbaum, R., ‘Four-dimensional topology: an introduction’, Bull. Amer. Math. Soc. 2 (1980), 1–159.

    Google Scholar 

  10. Milnor, J. W., ‘Microbundles and differentiable structures’, Notes, Princeton Univ. Press, Princeton, N.J., 1961.

    Google Scholar 

  11. Milnor, J. W. and Moore, J. C., ‘On the structure of Hopf algebras’, Ann. Math. 81 (1965), 211–264.

    MATH  Google Scholar 

  12. Orlik, P., Seifert Manifolds, Lecture Notes in Math. 291, Springer-Verlag, Berlin, Heidelberg, New York, 1972.

    Google Scholar 

  13. Scott, P., ‘The classification of compact 3-manifolds’, Proc. Conf. on Topology in Low Dimension, Bangor 1979, London Math. Soc. Lecture Notes 48 (1982), 3–-7.

  14. Spanier, E. H., Algebraic Topology, McGraw-Hill, New York, 1966.

    Google Scholar 

  15. Stasheff, J., ‘A classification theorem for fibre spaces’, Topology 2 (1963), 239–246.

    Google Scholar 

  16. Wall, C. T. C., Surgery on Compact Manifolds, Academic Press, London, New York, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cavicchioli, A., Meschiari, M. Idempotent comultiplications on graded algebras. Geom Dedicata 41, 251–274 (1992). https://doi.org/10.1007/BF00147455

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00147455

Keywords

Navigation