Annali di Matematica Pura ed Applicata

, Volume 136, Issue 1, pp 15–24 | Cite as

The topology of indefinite flag manifolds

  • M. Barros
  • S. Montiel
  • A. Romero


In this paper, we will use some techniques in Morse Theory in order to compute the Betti numbers of an indefinite flag manifold. The problem is reduced to compute it for the definite flag manifolds.


Betti Number Morse Theory Flag Manifold 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    M. Barros,On the almost Hermitian structures on a differentiable manifold, Ann. Mat. Pura Appl.,123 (1980), pp. 27–33.Google Scholar
  2. [2]
    M. Barros -A. Romero,Indefinite Kählerian manifolds, Math. Ann.,261 (1982), pp. 55–62.Google Scholar
  3. [3]
    M. Barros -F. Urbano,Differential Geometry of U(p+q+r)/U(p)xU(q)xU(r), Rend. Circ. Mat. Palermo,30 (1981), pp. 83–96.Google Scholar
  4. [4]
    R. Bott -H. Samelson,Applications of the theory of Morse to symmetric spaces, Amer. J. Math.,80 (1958), pp. 964–1029.Google Scholar
  5. [5]
    R.Bott,Morse theory and its applications to Homotopy Theory (Notes by A. van de Ven), Als manuskript vervielfältigt im Mathematischen Institut der Universitat Bonn, 1960.Google Scholar
  6. [6]
    C.Chevalley,Theory of Lie Groups I, Princ. Univ. Press, 1946.Google Scholar
  7. [7]
    T. Hangan,A Morse function on Grassmann manifolds, J. of Diff. Geom.,2 (1968), pp. 363–367.Google Scholar
  8. [8]
    S. Kobayashi -K. Nomizu,Foundations of differential Geometry I, II, Wiley-Inters., New York, 1963, 1969.Google Scholar
  9. [9]
    A. T.Lundell - S.Weingram,The topology of CW-complexes, Van Nostrand Reinhold Co., 1969.Google Scholar
  10. [10]
    J.Milnor,Morse theory, Annals of Math. stud., Princ. Univ. Press., 1963.Google Scholar
  11. [11]
    J. H. C. Whitehead,Combinatorial Homotopy I, Bull. of Amer. Math. Soc.,55 (1949), pp. 213–245.Google Scholar
  12. [12]
    J. A.Wolf,Spaces of constant curvature, Publish or Perish Inc., 1974.Google Scholar

Copyright information

© Fondazione Annali di Matematica Pura ed Applicata 1984

Authors and Affiliations

  • M. Barros
    • 1
  • S. Montiel
    • 1
  • A. Romero
    • 1
  1. 1.GranadaSpain

Personalised recommendations