Israel Journal of Mathematics

, Volume 111, Issue 1, pp 77–92 | Cite as

Lagrange transformations and duality for corner and flag singularities



Singularities on a space with a fixed collection of subspaces are studied. Homological objects for the singularities are constructed. A Lagrange transformation of the singularities is defined. It is shown that on the set of the isolated singularities, the Lagrange, transformation is an involution realizing the duality of corresponding homological objects.


Isomorphism Class Boundary Singularity Corner Singularity Barycentric Subdivision Cellular Decomposition 
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]
    V. I. Arnold,Critical points of functions on a manifold with a boundary, the simple Lie groups B k,C k,F 4,, Russian Mathematical Surveys33 (1978), 91–105.Google Scholar
  2. [2]
    J.-P. Brasselet,Définition combinatoire des homomorphismes de Poincaré, Alexander et Thom pour une pseudo variété. Asterisque82–83 (1981), 71–91.MathSciNetGoogle Scholar
  3. [3]
    J. A. Carlson,Polyhedral resolutions of algebraic varieties, Transactions of the American Mathematical Society292 (1985), 595–612.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    N. T. Dai, N. H. Duc and F. Pham,Singularités nondégénérées des systémes de Gauss-Manin, Memoire de la Societé Mathématique de France, Novelle Serie6 (1981), 85 pp.Google Scholar
  5. [5]
    A. S. Kryukovskii and D. V. Rastiagaev,Classification of unimodal and bimodal corner singularities, Funktional’nyi Analiz i ego Prilozheniya26 (1992), 213–215.Google Scholar
  6. [6]
    I. Scherback,Duality of boundary singularities, Rusian Mathematical Surveys39, (1984), 195–196.CrossRefGoogle Scholar
  7. [7]
    I. Scherback,Singularities in presence of symmetries, American Mathematical Society Translations, Series 2 (Topics in Singularity Theory)180 (1997), 189–196.Google Scholar
  8. [8]
    I. Sherbak,Symmetric and flag singularities, in preparation.Google Scholar
  9. [9]
    I. Scherback and A. Szpirglas,Boundary singularities: topology and duality, Advances in Soviet Mathematics21 (1994), 213–223.Google Scholar
  10. [10]
    D. Siersma,Singularities of functions on boundaries, corners, etc., Quarterly Journal of Mathematics. Oxford. Second Series,32 (1981), 119–127.MATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    A. Szpirglas,Singularités de bord: dualité, formules de Picard Lefschetz relatives et diagrammes de Dynkin, Bulletin de la Société Mathématique de France118 (1990), 451–486.MATHMathSciNetGoogle Scholar
  12. [12]
    A. Szpirglas,Diagrammes homologiques de variation et singularités de coin, Prépublication mathématique, Université Paris Nord,97-11 (1997).Google Scholar
  13. [13]
    V. M. Zakalukin,Singularities of circle contact with surface and flags, Functional Analysis and its Applications31 (1997), 73–76.CrossRefGoogle Scholar

Copyright information

© Hebrew University 1999

Authors and Affiliations

  1. 1.School of Mathematical SciencesTel Aviv UniversityTel AvivIsrael
  2. 2.LAGA, URA CNRS no 742Institut GaliléeVilletaneuseFrance

Personalised recommendations