Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

RELATIVE GOTTLIEB GROUPS OF THE PLÜCKER EMBEDDING OF SOME COMPLEX GRASSMANIANS

  • Gatsinzi, Jean B. (Department of Mathematics and Statiscal Sciences Botswana International University of Science and Technology) ;
  • Onyango-Otieno, Vitalis (Strathmore Institute of Mathematical Sciences Strathmore University) ;
  • Otieno, Paul A. (Strathmore Institute of Mathematical Sciences Strathmore University)
  • Received : 2018.11.05
  • Accepted : 2019.01.03
  • Published : 2020.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

Let Gr(k, n) be the Grassmann manifold of k-linear sub-spaces in ℂn. We compute rational relative Gottlieb groups of the Plücker embedding i : Gr(2, n) → ℂPN-1, where N = n(n - 1)/2.

Keywords

References

  1. U. Buijs and A. Murillo, The rational homotopy Lie algebra of function spaces, Comment. Math. Helv. 83 (2008), no. 4, 723-739. https://doi.org/10.4171/CMH/141
  2. P. Deligne, P. Griffiths, J. Morgan, and D. Sullivan, Real homotopy theory of Kahler manifolds, Invent. Math. 29 (1975), no. 3, 245-274. https://doi.org/10.1007/BF01389853
  3. Y. Felix, S. Halperin, and J.-C. Thomas, Rational Homotopy Theory, Graduate Texts in Mathematics, 205, Springer-Verlag, New York, 2001. https://doi.org/10.1007/978-1-4613-0105-9
  4. D. H. Gottlieb, Evaluation subgroups of homotopy groups, Amer. J. Math. 91 (1969), 729-756. https://doi.org/10.2307/2373349
  5. P. Hilton, J. Roitberg, and R. Steiner, On free maps and free homotopies into nilpotent spaces, in Algebraic topology (Proc. Conf., Univ. British Columbia, Vancouver, B.C., 1977), 202-218, Lecture Notes in Math., 673, Springer, Berlin, 1978.
  6. M. Hoffman, Endomorphisms of the cohomology of complex Grassmannians, Trans. Amer. Math. Soc. 281 (1984), no. 2, 745-760. https://doi.org/10.2307/2000083
  7. R. Kwashira, A note on derivations of a Sullivan model, Commun. Korean Math. Soc. 34 (2019), no. 1.
  8. K. Y. Lee and M. H. Woo, The G-sequence and the !-homology of a CW-pair, Topology Appl. 52 (1993), no. 3, 221-236. https://doi.org/10.1016/0166-8641(93)90104-L
  9. G. Lupton and S. B. Smith, Rationalized evaluation subgroups of a map. I. Sullivan models, derivations and G-sequences, J. Pure Appl. Algebra 209 (2007), no. 1, 159-171. https://doi.org/10.1016/j.jpaa.2006.05.018
  10. S. MacLane, Homology, Springer-Verlag, Berlin, New York, 1995.
  11. A. Murillo, The top cohomology class of classical compact homogeneous spaces, Algebras Groups Geom. 16 (1999), no. 4, 531-550.
  12. P. Otieno, J.-B. Gatsinzi, and V. Onyango-Otieno, Rational homotopy of mappings between Grassmannians, Quaestiones Math., to appear.
  13. J. Z. Pan and M. H. Woo, Exactness of G-sequences and monomorphisms, Topology Appl. 109 (2001), no. 3, 315-320. https://doi.org/10.1016/S0166-8641(99)00178-9
  14. D. Quillen, Rational homotopy theory, Ann. of Math. (2) 90 (1969), 205-295. https://doi.org/10.2307/1970725
  15. H. Shiga and M. Tezuka, Rational fibrations, homogeneous spaces with positive Euler characteristics and Jacobians, Ann. Inst. Fourier (Grenoble) 37 (1987), no. 1, 81-106. http://www.numdam.org/item?id=AIF_1987__37_1_81_0 https://doi.org/10.5802/aif.1078
  16. D. Sullivan, Infinitesimal computations in topology, Inst. Hautes Etudes Sci. Publ. Math. No. 47 (1977), 269-331. http://www.numdam.org/item?id=PMIHES_1977__47__269_0
  17. M. H. Woo and J.-R. Kim, Certain subgroups of homotopy groups, J. Korean Math. Soc. 21 (1984), no. 2, 109-120.
  18. M. H. Woo and K. Y. Lee, On the relative evaluation subgroups of a CW-pair, J. Korean Math. Soc. 25 (1988), no. 1, 149-160.