Skip to main content Accessibility help
×
Home

GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS

  • ZORAN Z. PETROVIĆ (a1) and BRANISLAV I. PRVULOVIĆ (a2)

Abstract

Groebner bases for the ideals determining mod $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}2$ cohomology of the real flag manifolds $F(1,1,n)$ and $F(1,2,n)$ are obtained. These are used to compute appropriate Stiefel–Whitney classes in order to establish some new nonembedding and nonimmersion results for the manifolds $F(1,2,n)$ .

    • Send article to Kindle

      To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

      Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

      Find out more about the Kindle Personal Document Service.

      GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS
      Available formats
      ×

      Send article to Dropbox

      To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

      GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS
      Available formats
      ×

      Send article to Google Drive

      To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

      GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS
      Available formats
      ×

Copyright

Corresponding author

References

Hide All
[1]Adams, W. W. and Loustaunau, P., An Introduction to Gröbner Bases, Graduate Studies in Mathematics, 3 (American Mathematical Society, Providence, RI, 1994).
[2]Ajayi, D. O. and Ilori, S. A., ‘Nonembeddings of the real flag manifolds R F (1, 1, n − 2)’, J. Aust. Math. Soc. (Ser. A) 66 (1999), 5155.
[3]Becker, T. and Weispfenning, V., Gröbner Bases: A Computational Approach to Commutative Algebra, Graduate Texts in Mathematics (Springer, New York, 1993).
[4]Borel, A., ‘La cohomologie mod 2 de certains espaces homogènes’, Comm. Math. Helv. 27 (1953), 165197.
[5]Buchberger, B., ‘A theoretical basis for the reduction of polynomials to canonical forms’, ACM SIGSAM Bull. 10/3 (1976), 1929.
[6]Hiller, H., ‘On the cohomology of real Grassmannians’, Trans. Amer. Math. Soc. 257 (1980), 521533.
[7]Korbaš, J. and Lörinc, J., ‘The ℤ2-cohomology cup-length of real flag manifolds’, Fund. Math. 178 (2003), 143158.
[8]Lam, K. Y., ‘A formula for the tangent bundle of flag manifolds and related manifolds’, Trans. Amer. Math. Soc. 213 (1975), 305314.
[9]Milnor, J. W. and Stasheff, J. D., Characteristic Classes, Annals of Mathematics Studies, 76 (Princeton University Press, New Jersey, 1974).
[10]Petrović, Z. Z. and Prvulović, B. I., ‘On Groebner bases and immersions of Grassmann manifolds G 2, n’, Homology Homotopy Appl. 13(2) (2011), 113128.
[11]Sanderson, B. J., ‘Immersions and embeddings of projective spaces’, Proc. Lond. Math. Soc. 14 (1964), 137153.
[12]Stong, R. E., ‘Cup products in Grassmannians’, Topology Appl. 13 (1982), 103113.
[13]Stong, R. E., ‘Immersions of real flag manifolds’, Proc. Amer. Math. Soc. 88 (1983), 708710.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

GROEBNER BASES AND NONEMBEDDINGS OF SOME FLAG MANIFOLDS

  • ZORAN Z. PETROVIĆ (a1) and BRANISLAV I. PRVULOVIĆ (a2)

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed