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Relative Gottlieb groups of the Pl\"ucker embedding of some complex Grassmanians

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Let $\Gr(k,n)$ be the Grassmann manifold of $k$-linear subspaces in $ \mathbb{C}^n$. We compute rational relative Gottlieb groups of the Pl\"ucker embedding $ i: \Gr(2, n)\rightarrow \mathbb{C}P^{N-1} $, where $ N= n(n-1)/2$.

Abstract

Let $\Gr(k,n)$ be the Grassmann manifold of $k$-linear subspaces in $ \mathbb{C}^n$. We compute rational relative Gottlieb groups of the Pl\"ucker embedding $ i: \Gr(2, n)\rightarrow \mathbb{C}P^{N-1} $, where $ N= n(n-1)/2$.

참고문헌 (18)

  1. U. Buijs, "The rational homotopy Lie algebra of function spaces", Comment. Math. Helv, 83(4), pp.723~739 (2008)[DOI]
  2. P. Deligne, "Real homotopy theory of Kahler manifolds", Invent. Math, 29(3), pp.245~274 (1975)[DOI]
  3. Y. Felix, "Rational Homotopy Theory" (2001), Springer-Verlag
  4. D. H. Gottlieb, "Evaluation subgroups of homotopy groups", Amer. J. Math., 91, pp.729~756 (1969)[DOI]
  5. P. Hilton, "On free maps and free homotopies into nilpotent spaces, in Algebraic topology (Proc. Conf., Univ. British Columbia, Vancouver, B.C., 1977)", Lecture Notes in Math., 673, pp.202~218 (1977), Springer
  6. M. Hoffman, "Endomorphisms of the cohomology of complex Grassmannians", Trans. Amer. Math. Soc, 281(2), pp.745~760 (1984)[DOI]
  7. Rugare Kwashira, "A note on derivations of a Sullivan model", 대한수학회논문집, 34(1), pp.279~286 (2019), 대한수학회[DOI]
  8. K. Y. Lee, "The G-sequence and the ω-homology of a CW-pair", Topology Appl, 52(3), pp.221~236 (1993)[DOI]
  9. G. Lupton, "Rationalized evaluation subgroups of a map. I. Sullivan models, derivations and G-sequences", J. Pure Appl. Algebra, 209(1), pp.159~171 (2007)[DOI]
  10. S. MacLane, "Homology" (1995), Springer-Verlag
  11. A. Murillo, "The top cohomology class of classical compact homogeneous spaces", Algebras Groups Geom, 16(4), pp.531~550 (1999)
  12. P. Otieno, "Rational homotopy of mappings between Grassmannians", Quaestiones Math
  13. J. Z. Pan, "Exactness of G-sequences and monomorphisms", Topology Appl., 109(3), pp.315~320 (2001)[DOI]
  14. D. Quillen, "Rational homotopy theory", Ann. of Math. (2), 90, pp.205~295 (1969)[DOI]
  15. H. Shiga, "Rational fibrations, homogeneous spaces with positive Euler characteristics and Jacobians", Ann. Inst. Fourier (Grenoble), 37(1), pp.81~106 (1987)
  16. D. Sullivan, "Infinitesimal computations in topology", Inst. Hautes Etudes Sci. Publ. Math., (47), pp.269~331 (1977)
  17. M. H. Woo, "Certain subgroups of homotopy groups", J. Korean Math. Soc, 21(2), pp.109~120 (1984)
  18. M. H. Woo, "On the relative evaluation subgroups of a CW-pair", J. Korean Math. Soc, 25(1), pp.149~160 (1988)

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