Skip to main content
Log in

Abstract

We consider certain natural (ℤ2)n actions on real Grassmann and flag manifolds andS 1 actions on complex Grassmann manifolds with finite stationary point sets and determine completely which of them bound equivariantly.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Atiyah M F and Singer I M, The index of elliptic operator-III.Ann. Math. 87 (1968) 546–604

    Article  MathSciNet  Google Scholar 

  2. Bott R E, Vector fields and characteristic number.Mich. Math. J. 14 (1967) 231–244

    Article  MATH  MathSciNet  Google Scholar 

  3. Conner, P E,Differentiable periodic maps. Lec. Notes in Math., 738 (Springer-Verlag) (1979)

  4. Kosniowski C and Stong R E, (ℤ2)k-Actions and characteristic numbers.Indiana Univ. Math. J. 28 (1979) 725–743

    Article  MATH  MathSciNet  Google Scholar 

  5. Lam K Y, A formula for the tangent bundle of flag manifolds and related manifolds.Trans. Am. Math. Soc. 213 (1975) 305–314

    Article  MATH  Google Scholar 

  6. Macdonald I G,Symmetric functions and Hall polynomials. (Oxford Mathematical Monographs) (1979)

  7. Mong S, The index of complex and quaternionic Grassmannians via Lefschetz formula.Adv. math. 15 (1975) 169–174

    Article  MATH  MathSciNet  Google Scholar 

  8. Sankaran P, Determination of Grassmann manifolds which are boundaries.Bull. Can. Math. 34 (1991) 119–122

    MATH  MathSciNet  Google Scholar 

  9. Sankaran P and Varadarajan K, Group actions on flag manifolds and cobordism.Can. J. Math. 45 (1993) 650–661

    MATH  MathSciNet  Google Scholar 

  10. Stong R E, Stationary point free group actions.Proc. Am. Math. Soc. 18 (1967) 1089–1092

    Article  MATH  MathSciNet  Google Scholar 

  11. Stong R E, Equivariant bordism and (ℤ2)k actions.Duke. Math. J. 37 (1972) 779–785

    Article  MathSciNet  Google Scholar 

  12. Stong, R E,Math. Reviews, 89d, 57050

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mukherjee, G. Equivariant cobordism of Grassmann and flag manifolds. Proc. Indian Acad. Sci. (Math. Sci.) 105, 381–391 (1995). https://doi.org/10.1007/BF02836873

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02836873

Keywords

Navigation