Evaluation Subgroups of Mapping Spaces over Grassmann Manifolds
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let Vk,n (C) denote the complex Steifel and Grk,n (C) the Grassmann mani folds for 1 ≤ k < n. In this paper, we compute, in terms of the Sullivan minimal models, the evaluation subgroups and, more generally, the relative evaluation subgroups of the fibration p : Vk,k+n (C) → Grk,k+n (C). In particular, we prove that G∗ (Grk,k+n (C), Vk,k+n (C) ; p) is isomorphic to G rel ∗ (Grk,k+n (C), Vk,k+n (C) ; p) ⊕ G∗ (Vk,k+n (C)).
Abstract
Let Vk,n (C) denote the complex Steifel and Grk,n (C) the Grassmann mani folds for 1 ≤ k < n. In this paper, we compute, in terms of the Sullivan minimal models, the evaluation subgroups and, more generally, the relative evaluation subgroups of the fibration p : Vk,k+n (C) → Grk,k+n (C). In particular, we prove that G∗ (Grk,k+n (C), Vk,k+n (C) ; p) is isomorphic to G rel ∗ (Grk,k+n (C), Vk,k+n (C) ; p) ⊕ G∗ (Vk,k+n (C)).
참고문헌 (11)
- Y. F´elix, "Rational Homotopy Theory, Graduate Texts in Mathematics", pp.205~ (2001), Springer-Verlag
- Y. F´elix, "Algebraic Models in Geometry 17" (2008), Oxford Graduate Texts in Mathematics
- D. H. Gottlieb, "A certain subgroup of the fundamental group", Amer. J. Math, 87, pp.840~856 (1965)
- 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)
- Oteng Maphane, "Rationalized evaluation subgroups of the complex Hopf fibration", 대한수학회논문집, 36(4), pp.835~840 (2021), 대한수학회[DOI]
- O. Maphane, "Derivations of a Sullivan model and the Rationalized G-Sequence", International J. of Math. and Math. Sci., 2021 (2021)
- S. B. Smith, "Rational evaluation subgroups", Math. Z, 221(3), pp.387~400 (1996)
- D. Sullivan, "Infinitesimal computations in topology", Publ. Math. IHES, 47, pp.269~331 (1977)
- M. H. Woo, "Certain subgroups of homotopy groups", J. Korean Math. Soc, 21(2), pp.109~120 (1984)
- M. H. Woo, "On the relative evaluation subgroups of a CW-pair", J. Korean Math. Soc, 25, pp.149~160 (1988)
- A. Zaim, "Relative Gottlieb groups of mapping spaces and their rational cohomology", Proc. Int. Geom. Cent, 15(1), pp.1~15 (2022)