Evaluation subgroups of a map and the rationalized $G$-sequence
DOI:
https://doi.org/10.52737/18291163-2022.14.2-1-10Բանալի բառեր:
Evaluation subgroups, Gottlieb group, $G$-sequenceԱմփոփում
In this paper, we determine, in terms of the Sullivan models, rational evaluation subgroups of the inclusion $ \mathbb{C} P(n)\hookrightarrow \mathbb{C} P(n+k) $ between complex projective spaces and, more generally, the $ G $-sequence of the homotopy monomorphism $ \iota: X\hookrightarrow Y $ between simply connected formal homogeneous spaces for which $ \pi_{\ast}(Y)\otimes \mathbb{Q}$ is finite dimensional.
Ներբեռնումներ
Հղումներ
Y. Félix, S. Halperin, and J.-C. Thomas, Rational homotopy theory, Springer, New York, (2001).
Y. Félix, J. Oprea, and D. Tanré, Algebraic models in geometry, Oxford University Press, New York, (2008).
D.H. Gottlieb, Evaluation subgroups of homotopy groups. Am. J. Math., 91 (1969), pp. 729-756.
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, pp. 159-171. https://doi.org/10.1016/j.jpaa.2006.05.018
O. Maphane, Derivations of a Sullivan model and the rationalized $G$-sequence. Int. J. Math. Math. Sci., (2021), Art. ID 6687527, 5 pp.
P.A. Otieno, J.-B. Gatsinzi and O.V. Otieno, Rationalized evaluation subgroups of mapping spaces between complex Grassmannians. Afr. Mat., 31 (2020), pp. 297-303. https://doi.org/10.1007/s13370-019-00724-w
J.Z. Pan and M.H. Woo, Exactness of $G$-sequences and monomorphisms. Topology Appl., 109 (2001), pp. 315-320.
D. Sullivan, Infinitesimal computations in topology. Publ. Math. IHES., 47 (1977), pp. 269-331.
E.H. Spanier, Algebraic topology, Springer-Verlag, New York, (1989). Corrected reprint of the 1966 original.
M.H. Woo and K.Y. Lee, On the relative evaluation subgroups of a CW-pair. J. Korean Math. Soc., 25 (1988), no. 1, pp. 149-160.
Ներբեռնումներ
Հրատարակվել է
Տարբերակներ
- 2023-09-16 (2)
- 2022-02-18 (1)
Թողարկում
Բաժին
Արտոնագհր
Copyright (c) 2022 Armenian Journal of Mathematics
Այս աշխատանքն արտոնագրված է որպես Creative Commons Attribution 4.0 International License.
