Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Topics on space-time topology

  • 66 Accesses

  • 2 Citations

Abstract

The orientability properties of space-times are analysed in detail using elementary algebraic methods. Time, space and charge orientability are discussed and various possible generalisations of charge orientability suggested. There is also a bundle-theoretic analysis of the first two topological properties together with a discussion of spinor-structures from the point of view of the Lorentz bundle of bases over a space-time. A section is devoted to some comments on the topologisation of certain space-times with topologies derived from their causal relations.

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

References

  1. Aharanov, Y. and Susskind, L. (1967).Physical Review,159, 1237.

  2. Borel, A. and Hirzebruch, F. (1959).American Journal of Mathematics,81, 315.

  3. Bott, R. and Mather, J. (1968).Proceedings of the Battelle Rencontres in Mathematics and Physics, 1967, ed. De-Witt, B. and Wheeler, J. A. W. A. Benjamin.

  4. Bräuer, H. J. (1971).International Journal of Theoretical Physics, Vol. 4, No. 4, p. 243.

  5. Brickell, F. and Clarke, R. S. (1970).Differentiable Manifolds. Van-Nostrand Reinhold.

  6. Eilenberg, S. (1963). Algebraic Topology.Lectures in Modern Mathematics, ed. Saaty, T. L. John Wiley and Sons.

  7. Eilenberg, S. and Maclane, S. (1947).Annals. of Mathematics,48(2).

  8. Geroch, R. (1968).Journal of Mathematical Physics,9(11), 1739.

  9. Geroch, R. (1969). Space-Time Structure from a Global Viewpoint.Proceedings of the Enrico-Fermi Summer School. Academic Press.

  10. Goldstein, R. Z. and Lininger, L. (1970).Proceedings of the 1969 Georgia Topology Institute, eds. Cantrell, and Edwards. Markham.

  11. Greenberg, M. J. (1967).Lectures on Algebraic Topology. W. A. Benjamin.

  12. Hicks, N. (1964).Notes on Differential Geometry. Van-Nostrand.

  13. Lichnerowicz, A. (1968). Topics on Space-Times.Proceedings of the Battelle Rencontres in Mathematics and Physics, 1967, ed. De-Witt, B. and Wheeler, J. A. W. A. Benjamin.

  14. Markus, L. (1955).Annals of Mathematics,63(2), 411.

  15. Maunder, C. R. F. (1970).Algebraic Topology. Van-Nostrand Reinhold.

  16. Michel, L. (1965). Relations Entre Symétries Intérnes et Invariance Relativiste.Proceedings of the Cargese summer school, 1965, ed. Lurçat, F. Gordon and Breach.

  17. Milnor, J. (1963).L'Ensiegnement Mathématique,9, 198.

  18. Penrose, R. (1964). A Conformal Treatment of Infinity.Relativity, Groups and Topology, ed. De-Witt, B. Gordon and Breach.

  19. Penrose, R. (1968). The Structure of Space-Time.Proceedings of the Battelle Rencontres in Mathematics and Physics, 1967, ed. De-Witt, B. and Wheeler, J. A. W. A. Benjamin.

  20. Porteous, I. R. (1969).Topological Geometry. Van-Nostrand Reinhold.

  21. Scott, W. (1964).Group Theory. Prentice-Hall.

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

  23. Steen, L. A. and Seebach, J. A. Jnr. (1970).Counterexamples in Topology. Holt, Rinehart and Winston, New York.

  24. Whiston, G. S. (1972).International Journal of Theoretical Physics, Vol. 6, No. 1, pp. 75–76.

  25. Zeeman, E. C. (1964).Journal of Mathematical Physics,5(4), 460.

Download references

Author information

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Whiston, G.S. Topics on space-time topology. Int J Theor Phys 8, 99–121 (1973). https://doi.org/10.1007/BF00678611

Download citation

Keywords

  • Field Theory
  • Elementary Particle
  • Quantum Field Theory
  • Causal Relation
  • Topological Property