Advertisement

Annals of Global Analysis and Geometry

, Volume 6, Issue 2, pp 141–163 | Cite as

On extensions of principal bundles

  • Kirill Mackenzie
Article

Keywords

Group Theory Principal Bundle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. D. Bleecker, Gauge theory and variational principles. Addison-Wesley, Reading, Mass. 1981.Google Scholar
  2. [2]
    R. Brown and C. B. Spencer, “G-groupoids, crossed modules and the fundamental groupoid of a topoligical group”. Proc. Konin, Nederl. Akad. van Wetens. A, 79, 296–302, 1976.Google Scholar
  3. [3]
    W. Greub and H. R. Petry, “On the lifting of structure groups”. Differential Geometrical Methods in Mathematical Physics II, 1977. Ed. K. Bleuler, H. R. Petry and A. Reetz. Lecture Notes in Mathematics # 676. Springer-Verlag, Berlin, 1978.Google Scholar
  4. [4]
    W. Greub, S. Halperin and R. Vanstone, Connections, Curvature and Cohomology, Vol. II. Academic Press, New York, 1973.Google Scholar
  5. [5]
    W. Greub, S. Halperin and R. Vanstone, Connections, Curvature and Cohomology, Vol. III. Academic Press, New York, 1976.Google Scholar
  6. [6]
    P. J. Higgins, Notes on Categories and Groupoids. van Nostrand-Reinhold, London, 1971.Google Scholar
  7. [7]
    G. Hochschild, “Group extensions of Lie groups, II”. Ann. of Math. (2) 54, 537–551, 1951.Google Scholar
  8. [8]
    S. Kobayashi and K. Nomizu, Foundations of differential geometry, Vols. I, II. Interscience, New York, 1963 and 1969.Google Scholar
  9. [9]
    K. Mackenzie, Lie groupoids and Lie algebroids in differential geometry. LMS Lecture Notes Series, no. 124. Cambridge Univ. Press. 1987.Google Scholar
  10. [10]
    K. Mackenzie “Integrability obstructions for extensions of Lie algebroids”. Cahiers de Topol. et Géom. Diff. Catégoriques, (to appear).Google Scholar
  11. [11]
    K. Mackenzie, Classification of principal bundles and Lie groupoids with prescribed gauge group bundle. Preprint.Google Scholar
  12. [12]
    J. Pradines, “Théorie de Lie pour les groupoides différentiables. Calcul différentiel dans la catégorie des groupoides infinitésimaux”. C. R. Acad. Sci. Paris. t. 264, 245–248, Série A, 1967.Google Scholar
  13. [13]
    A. Shapiro, “Group extensions of compact Lie groups’. Ann. of Math. (2) 50, 581–586, 1949.Google Scholar
  14. [14]
    N. Teleman, “A characteristic ring of a Lie algebra extension”. Accad. Naz. Lincei. Rend. Cl. Sci. Fis. Mat. Natur. (8) 52, 498–506 and 708–711, 1972.Google Scholar

Copyright information

© VEB Deutscher Verlag der Wissenschaften 1988

Authors and Affiliations

  • Kirill Mackenzie
    • 1
  1. 1.Department of Mathematical SciencesUniversity of Durham Science LaboratoriesDurhamEngland

Personalised recommendations