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

Oteng Maphane

doi:10.52737/18291163-2022.14.2-1-10

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.

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