Home The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds
Article
Licensed
Unlicensed Requires Authentication

The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds

  • Vimala Ramani
Published/Copyright: October 7, 2023
Become an author with De Gruyter Brill
Author Information Explore this Subject
Mathematica Slovaca
From the journal Mathematica Slovaca Volume 73 Issue 5

ABSTRACT

We compute the rational zero-divisor cup-length of the oriented partial flag manifold F˜(n1,…,nk) of type (n1,…, nk), k ≥ 2. For certain classes of oriented partial flag manifolds, we compare the rational zero-divisor cup-length and the ℤ2-zero-divisor cup-length.

2020 Mathematics Subject Classification: 57R19; 57T15; 55M30
Keywords: oriented partial flag manifolds; zero-divisor cup-length; characteristic classes; topological complexity

Dedicated to the memory of Professor Július Korbaš with respect

(Communicated by Tibor Macko)

Acknowledgement

The author thanks Professor Parameswaran Sankaran for the constant encouragement and very valuable and illuminating discussions. The author thanks the anonymous referee for very careful reading of the manuscript and very helpful comments and suggestions due to which the paper is more detailed and complete.

References

[1] Borel, A.: Sur la cohomologie des espaces fibrs principaux et des espaces homognes de groupes de Lie compacts, Ann. Math. 57(2) (1953), 115–207.10.2307/1969728Search in Google Scholar

[2] Borel, A.: Kählerian coset spaces of semi-simple Lie groups, Proc. Nat. Acad. Sci. U.S.A. 40(12) (1954), 1147–1151.10.1073/pnas.40.12.1147Search in Google Scholar PubMed PubMed Central

[3] Bruner, R. R.—Catanzaro, M.—May J. P.: Characteristic Cclasses, lecture notes available at http: //www.math.uchicago.edu/may/CHAR/charclasses.pdf.Search in Google Scholar

[4] Cohen, D.—Suciu, A.: Boundary manifolds of projective hypersurfaces, Adv. Math. 206 (2006), 538–566.10.1016/j.aim.2005.10.003Search in Google Scholar

[5] Davis, D.: On the zero-divisor-cup-length of planar polygon spaces modulo oriented isometry, Topology Appl. 207 (2016), 43–53.10.1016/j.topol.2016.04.018Search in Google Scholar

[6] Farber, M.: Topological complexity of motion planning, Discrete Comput. Geom. 29 (2003), 211–221.10.1007/s00454-002-0760-9Search in Google Scholar

[7] Farber, M.—Tabachnikov, S.—Yuzvinsky, S.: Topological robotics: motion planning in projective spaces, Int. Math. Res. Not. IMRN 2003(34) (2003), 1853–1870.10.1155/S1073792803210035Search in Google Scholar

[8] Farber, M.: Instabilities of robot motion, Topology Appl. 140 (2004), 245–266.10.1016/j.topol.2003.07.011Search in Google Scholar

[9] He, C.: Cohomology rings of the real and oriented partial flag manifolds, Topology Appl. 279 (2020), Art. ID 107239.10.1016/j.topol.2020.107239Search in Google Scholar

[10] Korbaš, J.—Lörinc, J.: The ℤ2-cohomology cup-length of real flag manifolds, Fund. Math. 178 (2003), 143–158.10.4064/fm178-2-4Search in Google Scholar

[11] Korbaš, J.: The cup-length of the oriented Grassmannians vs a new bound for zero-cobordant manifolds, Bull. Belg. Math Soc. Simon Stevin 17 (2010), 69–81.10.36045/bbms/1267798499Search in Google Scholar

[12] Korbaš, J.—Rusin, T.: A note on the ℤ2-cohomology algebra of oriented Grassmann manifolds, Rend. Circ. Mat. Palermo, II. Ser 65(3) (2016), 507–517.10.1007/s12215-016-0249-7Search in Google Scholar

[13] Kotschick, D.—Terzlc, S.: On formality of generalized symmetric spaces, Math. Proc. Cambridge Phil. Soc. 134(3) (2003), 491–505.10.1017/S0305004102006540Search in Google Scholar

[14] Miller, C.: The topology of rotation groups, Ann. Math. 57(2) (1953), 90–114.10.2307/1969727Search in Google Scholar

[15] Ramani, V.: On the topological complexity of Grassmann manifolds, Math. Slovaca 70(5) (2020), 1197–1210.10.1515/ms-2017-0425Search in Google Scholar

[16] Ramani, V.—Sankaran, P.: On degrees of maps between Grassmannians, Proc. Indian Acad. Sci. Math.Sci. 107(1) (1997), 13–19.10.1007/BF02840469Search in Google Scholar

[17] Stong, R. E.: Cup-products in Grassmannians, Topology Appl. 13 (1982), 103–113.10.1016/0166-8641(82)90012-8Search in Google Scholar

[18] Stong, R. E.: Semicharacteristics of oriented Grassmannians, J. Pure Appl. Algebra 33 (1984), 97–103.10.1016/0022-4049(84)90029-XSearch in Google Scholar
Received: 2021-12-24
Accepted: 2023-02-03
Published Online: 2023-10-07

© 2023 Mathematical Institute Slovak Academy of Sciences

Articles in the same Issue

  1. Remembering Professor Štefan Znám, 9.2.1936–17.7.1993
  2. Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures
  3. Enlargements of Quantales
  4. Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
  5. Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet L-Functions
  6. On the Rational Parametric Solution of Diagonal Quartic Varieties
  7. Theory of Certain Non-Univalent Analytic Functions
  8. Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)
  9. A Conjecture on H3(1) for Certain Starlike Functions
  10. Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces
  11. Complete Monotonicity and Inequalities Involving the k-Gamma and k-Polygamma Functions
  12. Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms
  13. On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
  14. On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces
  15. The Lehmann Type II Teissier Distribution
  16. Asymptotic Predictive Inference of Negative Lower Tail Index Distributions
  17. On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law
  18. The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds
https://doi.org/10.1515/ms-2023-0097
Keywords for this article
oriented partial flag manifolds; zero-divisor cup-length; characteristic classes; topological complexity

Articles in the same Issue

  1. Remembering Professor Štefan Znám, 9.2.1936–17.7.1993
  2. Chordal and Perfect Zero-Divisor Graphs of Posets and Applications to Graphs Associated with Algebraic Structures
  3. Enlargements of Quantales
  4. Multiplicative Dependent Pairs in the Sequence of Padovan Numbers
  5. Dirichlet Series with Periodic Coefficients, Riemann’s Functional Equation, and Real Zeros of Dirichlet L-Functions
  6. On the Rational Parametric Solution of Diagonal Quartic Varieties
  7. Theory of Certain Non-Univalent Analytic Functions
  8. Initial Coefficients and Fekete-Szegő Inequalities for Functions Related to van der Pol Numbers (VPN)
  9. A Conjecture on H3(1) for Certain Starlike Functions
  10. Coefficient Problems of Quasi-Convex Mappings of Type B on the Unit Ball in Complex Banach Spaces
  11. Complete Monotonicity and Inequalities Involving the k-Gamma and k-Polygamma Functions
  12. Study of Oscillation Criteria of Odd-Order Differential Equations with Mixed Neutral Terms
  13. On a System of Difference Equations Defined by the Product of Separable Homogeneous Functions
  14. On the Existence of Bi-Lipschitz Equivalent Metrics in Semimetric Spaces
  15. The Lehmann Type II Teissier Distribution
  16. Asymptotic Predictive Inference of Negative Lower Tail Index Distributions
  17. On Numerical Problems in Computing Life Annuities Based on the Makeham–Beard Law
  18. The Rational Zero-Divisor Cup-Length of Oriented Partial Flag Manifolds
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 29.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/ms-2023-0097/html
Scroll to top button