Articles

HOMOLOGY RIGIDITY OF GRASSMANNIANS

  • LI Fang ,
  • DUAN Hai-Bao
Expand
  • Department of Mathematics, Jilin University, Changchun 130024, China;Institute of Mathematics &|Key Laboratory of Mathematics Mechanization, Chinese Academy of Sciences, Beijing 100190, China

Received date: 2008-12-22

  Online published: 2009-05-20

Supported by

Supported by NSFC (10631060)

Abstract

Applying the theory of Gr¨obner basis to the Schubert presentation for the cohomology of Grassmannians [2], we extend the homology rigidity results known for the classical Grassmanians to the exceptional cases.

Key words: Grassmannians; cohomology

Cite this article

LI Fang , DUAN Hai-Bao . HOMOLOGY RIGIDITY OF GRASSMANNIANS[J]. Acta mathematica scientia, Series B, 2009 , 29(3) : 697 -704 . DOI: 10.1016/S0252-9602(09)60065-5

References


[1] Duan H. Self-maps of the Grassmannian of complex structures. Compositio Math, 2002, 132: 159–175


[2] Duan H, Zhao Xuezhi. The Chow rings of generalized Grassmannians. arXiv: math.AG/0511332


[3] Duan H, Zhao Xuezhi. The integral cohomology of complete flag manifolds. arXiv: math.AT/0801.2444


[4] Ernic K. A Guide To Maple. Springer-Verlag, 1999


[5] Glover H, Homer W. Self-maps of flag manifolds. Trans AMS, 1981, 267: 423–434


[6] Hoffman M. Endomorphisms of the cohomology of complex Grassmannians. Trans AMS, 1984, 281: 745–740


[7] Hoffman M. On fixed point free maps of the complex flag manifold. Indiana Math J, 1984, 33: 249–255


[8] Humphreys J E. Introduction to Lie algebras and representation theory. Graduated Texts in Math 9. New
York: Springer-Verlag, 1972


[9] Li F. Endomorphisms of the cohomology ring of a generalized Grassmannian
[D]. Changchun: Jilin Uni-
versity, 2008


[10] Papadima S. Rigidity properties of compact Lie groups modulo maximal tori. Math Ann, 1987, 275:
637–652

Outlines

/