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Topology and cosmology

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References

  1. Whitney, H. (1936).Annals of Maths.,37, 645, 865.

    Article  MATH  MathSciNet  Google Scholar 

  2. Geroch, R. (1968).J. Math. Phys.,9, 1739.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  3. Kobayashi, S. and Nomizu, K. (1963).Foundations of Differential Geometry, Interscience, New York.

    MATH  Google Scholar 

  4. Steenrod, N. (1951).The Topology of Fibre Bumllkes, Princeton.

  5. Markus, L. (1955).Annals of Maths.,62, 411.

    Article  MATH  MathSciNet  Google Scholar 

  6. Fierz, M. and Jost, R. (1965).Rev. Phys. Act.,38, 137.

    MATH  Google Scholar 

  7. Bass, R. and Witten, L. (1957).Rev. Mod. Phys.,29, 452.

    Article  MathSciNet  ADS  Google Scholar 

  8. Geroch, R. (1967).J. Math. Phys.,8, 782.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  9. Kronheimer, E. and Penrose, R. (1967).Proc. Camb. Phil. Soc.,63, 481.

    Article  MATH  MathSciNet  Google Scholar 

  10. Penrose, R. (1968). ‘Structure of Space-Time’. InBattelle Rencontress (Ed. C. de Witt and J. Wheeler), Benjamin, New York.

    Google Scholar 

  11. Hawking, S. (1968).Proc. Roy. Soc. A,308, 433.

    ADS  Google Scholar 

  12. Geroch, R. (1967). Ph.D. Thesis, Princeton University.

  13. Teldovich, Ya. B. and Novikov, I. D. (1967).J.F.T.P. Letter,6, 236.

    ADS  Google Scholar 

  14. Markus, L. (1965).Rev. Roum. Math. Pures et Appl.,X, 1089.

    MathSciNet  Google Scholar 

  15. Lichnérowicz, A. InBattelle Rencontres (see [10]) (.

    Google Scholar 

  16. Aharonov, Y. and Susskind, I. (1967).Phys. Rev.,158, 1237.

    Article  ADS  Google Scholar 

  17. Bichteler, K. (1968).J. Math. Phys.,9, 813.

    Article  MATH  ADS  Google Scholar 

  18. Geroch, R. (1970).J. Math. Phys.,11, 343.

    Article  MATH  ADS  Google Scholar 

  19. Clarke, C. J. S. (1970).Proc. Roy. Soc. A,314, 417.

    MATH  ADS  Google Scholar 

  20. Hawking, S. W. and Ellis, G. F. R. (1968).Ap. J.,152, 25. See also a forthcoming book to be published by the Cambridge University Press.

    Article  ADS  Google Scholar 

  21. Ellis, G. F. R. (1969). Lectures at International School of Physics, Varenna, Corso XI. VII (to be published).

    Google Scholar 

  22. Wolf, J. A. (1967),Spaces of Constant Curvature, McGraw-Hill, New York.

    MATH  Google Scholar 

  23. Auslander, I. and Markus, I. (1958).Memoir 30, American Math. Soc.

  24. Calabi, E. and Markus, I. (1962).Annals of Maths.,75, 63.

    Article  MATH  MathSciNet  Google Scholar 

  25. Schroedinger, F. (1956),Anpanding Universes, Cambridge University Press.

  26. Heckmann, O. and Schucking, E. (1959). ‘Newtonsche und Einsteinsche Kosmologie’,Handbuch d. Physik,LIII, 489: (1962), ‘Relativistic Cosmology’. InGravitation. (Ed. L. Witten). Wiley, New York.

    ADS  Google Scholar 

  27. Robertson, H. P. (1933).Rev. Mod. Phys.,5, 62.

    Article  MATH  ADS  Google Scholar 

  28. Bondi, H. (1960).Cosmology, Cambridge University Press.

  29. Killing, W. (1891).Math. Annalen,39, 257.

    Article  MATH  MathSciNet  Google Scholar 

  30. Klein, F. (1928),Vorlesungen uber Nicht-Euklidische Geometrie, Springer.

  31. Rinow, W. (1961).Die Innere Geometrie der Metrischem Räume, Springer.

  32. Ellis, G. F. R. and MacCallum, M. A. H. (1969).Comm. Math. Phys.,12, 108.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  33. Schmidt, B. (1969).Comm. Math. Phys.,15, 329.

    Article  MathSciNet  ADS  Google Scholar 

  34. Ellis, G. F. R. (1967).J. Math. Phys.,8, 1171.

    Article  ADS  Google Scholar 

  35. Lobell, F. (1931). Ber. Verhand. Sächs. Akad. Wiss. Leipzig,Math. Phys., Kl., 83, 167.

    Google Scholar 

  36. Garner, C. (1970).Proc. Roy. Soc. A,316, 441.

    MATH  MathSciNet  ADS  Google Scholar 

  37. Yano, K. and Bochner, S. (1953). ‘Curvature and Betti Numberg'sAnnals of Maths Study No. 32, Princeton University Press

  38. Kantowski, R. and Sachs, R. K. (1966).J. Math. Phys.,7, 443.

    Article  MathSciNet  ADS  Google Scholar 

  39. MacCallum, M. A. H. and Ellis, G. F. R. (1970).Comm. Math. Phys.,19, 31.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  40. Misner, C. W. (1969).Phys. Res. Lett.,22, 1071; (1970). Article inRelativity, Plenum Press

    Article  MATH  ADS  Google Scholar 

  41. Solheim, J. E. (1968).Nature,217, 41, and (1968),219, 45; see also Dehnen H. and Hönl, H. (1968).Naturwissenschaft,55, 413; Reinhardt, M. Von. (1969),Naturwissenschaft,56, 323; Petrosian, V. and Ekers, R. D., (1969).Nature,224, 484.

    Article  ADS  Google Scholar 

  42. Audretsch, J. and Dehnen, H. (1969).Astron. and Astrophys.,3, 252.

    ADS  Google Scholar 

  43. Kundt, W. (1967).Comm. Math. Phys.,4, 143.

    Article  MATH  ADS  MathSciNet  Google Scholar 

  44. Sachs, R. K. and Wolfe, A. M. (1967).Ap. J.,147, 73.

    Article  ADS  Google Scholar 

  45. Rees, M. (1969). Lectures at Varenna, see [21]. —.

    Google Scholar 

  46. Rees, M. and Sciama, D. W. (1968).Nature,217, 511.

    Article  ADS  Google Scholar 

  47. Kantowski, R. (1969).Ap. J.,155, 89.

    Article  ADS  Google Scholar 

  48. Kundt, W. (1968). ‘Recent Progress in Cosmology’,Springer Tracts in Modern Physics,47, Springer.

  49. Hawking, S. W. and Penrose, R. (1970).Proc. Roy. Soc. A,314, 529.

    MATH  MathSciNet  ADS  Google Scholar 

  50. Geroch, R. (1968).J. Math. Phys.,9, 450; (1968).Annals of Physics,48, 526: (1970). Article inRelativity, Plenum Press.

    Article  MATH  MathSciNet  ADS  Google Scholar 

  51. Schmidt, B. Gwatt conference talk.

  52. Geroch, R. (1970).J. Math. Phys.,11, 437.

    Article  MathSciNet  MATH  ADS  Google Scholar 

  53. Seifert, H. J. (1967).Comm. Math. Phys.,4, 324: (1967).Zs. fur Naturfor.,22a, 1356; Ph. D. Thesis. Hamburg University (1968).

    Article  MathSciNet  ADS  Google Scholar 

  54. Boyer, R. H. (1964).Nuoro Cimento,33, 345.

    MATH  MathSciNet  Google Scholar 

  55. Misner, C. W. (1967). InLectures in Applied Maths, Vol. 8 (Ed. J. Ehlers, Am. Math. Soc.).

  56. Einstein, A. InThe Principle of Relativity, Dover Publications Reprint (New York).

  57. Avez, A. (1962).C.R. Acad. Sci. t. 254, 3984; Thesis, University of Paris Faculty of Science (1964). See also Deminaski, M. and Woronowicz, S. (1967).Bull. Acad. Polon. Sci.,XV, 355.

    MATH  MathSciNet  Google Scholar 

  58. Milnor, J. (1963). ‘Morse Theory’,Annals of Maths Studies, No. 51, Princeton University Press.

  59. Sciama, D. W. (1969). Lectures at Varenna, see [21]. —.

    Google Scholar 

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  1. Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge

    G. F. R. Ellis

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Read on 18 May 1970 at the Gwatt Seminar on the Bearings of Topology upon General Relatixity

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Ellis, G.F.R. Topology and cosmology. Gen Relat Gravit 2, 7–21 (1971). https://doi.org/10.1007/BF02450512

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