Evaluation subgroups of a map and the rationalized $G$-sequence

Authors

  • Oteng Maphane Botswana International University of Science and Technology

DOI:

https://doi.org/10.52737/18291163-2022.14.2-1-10

Keywords:

Evaluation subgroups, Gottlieb group, $G$-sequence

Abstract

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.

 

Editorial Board's note. We inform our readers that J.-B. Gatsinzi mentions in his work, published in Armen. J. Math. vol. 15, no. 9, 2023, that O. Maphane's paper contains a mistake. According to Gatsinzi, his Corollary 1 corrects Theorem 2.2 of the current paper. We contacted Maphane on this issue, and he agreed with Gatzinzi's statement.

References

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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

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Published

2022-02-18 — Updated on 2023-09-16

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How to Cite

Evaluation subgroups of a map and the rationalized $G$-sequence. (2023). Armenian Journal of Mathematics, 14(2), 1-10. https://doi.org/10.52737/18291163-2022.14.2-1-10 (Original work published 2022)