Skip to main content
SpringerLink
Log in

Vector fields and cohomology of G/P

  • Conference paper
  • First Online:
Group Actions and Vector Fields

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 956))

Abstract

We discuss the cohomology rings of homogeneous spaces from the viewpoint of zeros of vector fields.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 29.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 39.95
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akyildiz, E., Ph.D. Thesis, Univ. of British Columbia, Vancouver, B.C., 1977.

    Google Scholar 

  2. ____, Vector fields and Equivariant bundles, Pac. Jour. of Math. 81 (1979), 283–289.

    Article  MathSciNet  MATH  Google Scholar 

  3. ____, A vector field with one zero on G/P, Proc. Amer. Math. Soc. 67 (1977), 32–34.

    MathSciNet  MATH  Google Scholar 

  4. ____, Bruhat decomposition via Gm-action, Bull. Acad. Pol. Sci., Sér. Sci., Math., 28 (1980), 541–547.

    MathSciNet  MATH  Google Scholar 

  5. ____, On the Gm-decomposition of G/P, METU Jour. Pure and Applied Sci., to appear.

    Google Scholar 

  6. Akyildiz, E. and Carrell, J.B., Zeros of holomorphic vector fields and the Gysin homomorphism, Proc. Symp. Pure Math. Summer Inst. on Singularities (Arcata), to appear.

    Google Scholar 

  7. Akyildiz, E. and Carrell, J.B., Gysin homomorphism of homogeneous spaces, submitted.

    Google Scholar 

  8. Akyildiz, E. and Carrell, J.B. and Lieberman, D.I. and Sommese, A.J., On the graded rings associated to holomorphic vector fields, to appear.

    Google Scholar 

  9. Bernstein, I.N. and Gel'fand, I.M. and Gel'fand, S.I., Schubert cells and cohomology of the space G/P, Russian Math. Surveys 28 (1973), 1–26.

    Article  MathSciNet  MATH  Google Scholar 

  10. Borel, A., Sur la cohomologie des espaces fibrés principaux et des espaces homogenes des groupes de Lie compacts, Ann. of Math (2) 57 (1953), 115–207.

    Article  MathSciNet  MATH  Google Scholar 

  11. Carrell, J.B., Vector fields and the cohomology of G/B, to appear.

    Google Scholar 

  12. Carrell, J.B. and Lieberman, D.I., Holomorphic vector fields and Kaehler manifolds, Invent. Math 21 (1974), 303–309.

    Article  MathSciNet  MATH  Google Scholar 

  13. Carrell, J.B. and Lieberman, D.I., Vector fields and Chern numbers, Math. Ann. 225 (1977), 263–273.

    Article  MathSciNet  MATH  Google Scholar 

  14. Carter, R.W., Simple groups of Life type, John Wiley and Sons, New York, 1972.

    Google Scholar 

  15. Chevalley, C., Invariants of finite groups generated by reflections, Amer. J. Math. 67 (1955), 778–782.

    Article  MathSciNet  MATH  Google Scholar 

  16. Griffiths, P. and Harris, H., Principles of Algebraic geometry, John Wiley and Sons, New York, 1978.

    MATH  Google Scholar 

  17. Humphreys, J.E., Linear algebraic groups, Springer-Verlag, Berlin and New York, 1975.

    Book  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, Ankara, Turkey

    Ersan Akyildiz

Authors
  1. Ersan Akyildiz
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

James B. Carrell

Rights and permissions

Reprints and permissions

Copyright information

© 1982 Springer-Verlag

About this paper

Cite this paper

Akyildiz, E. (1982). Vector fields and cohomology of G/P. In: Carrell, J.B. (eds) Group Actions and Vector Fields. Lecture Notes in Mathematics, vol 956. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0101504

Download citation

  • DOI: https://doi.org/10.1007/BFb0101504

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-11946-3

  • Online ISBN: 978-3-540-39528-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation