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Lee, Kee Young;Yoon, Young Joong
- Journal of the Chungcheong Mathematical Society
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- v.9 no.1
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- pp.89-99
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- 1996
We introduce and study certain subgroups of homotopy groups which contain evaluation subgroups and use these subgroups to obtain a sequence similar to homotopy sequence of fibration. We use the sequence to calculate evaluation subgroups or generalized evaluation subgroups of some topological pair.
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Oteng Maphane
- Communications of the Korean Mathematical Society
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- v.38 no.1
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- pp.257-266
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- 2023
Let G_k,n(ℍ) for 2 ≤ k < n denote the Grassmann manifold of k-dimensional vector subspaces of ℍⁿ. In this paper, we determine the evaluation subgroups of the Plüker embedding $G{_{2,n}}({\mathbb{H}}){\hookrightarrow}{\mathbb{H}}P^{N-1}$, where $N\;=\;({n \atop 2}\)$.
https://doi.org/10.4134/CKMS.c220028 인용 PDF

Abdelhadi Zaim
- Kyungpook Mathematical Journal
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- v.63 no.1
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- pp.131-139
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- 2023
Let V_k,n (ℂ) denote the complex Steifel and Gr_k,n (ℂ) the Grassmann manifolds 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 : V_k,k+n (ℂ) → Gr_k,k+n (ℂ). In particular, we prove that G_* (Gr_k,k+n (ℂ), V_k,k+n (ℂ) ; p) is isomorphic to G^rel_* (Gr_k,k+n (ℂ), V_k,k+n (ℂ) ; p) ⊕ G_* (V_k,k+n (ℂ)).
https://doi.org/10.5666/KMJ.2022.63.1.131 인용 PDF

Maphane, Oteng
- Communications of the Korean Mathematical Society
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- v.36 no.4
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- pp.835-840
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- 2021
In this paper, we compute the rational evaluation subgroup of the Hopf fibration S²ⁿ⁺¹ ↪ ℂP(n). We show that, for the Sullivan model 𝜙 : A → B, where A and B are the minimal Sullivan models of ℂP(n) and S²ⁿ⁺¹ respectively, the evaluation subgroup G_n(A, B; 𝜙) and the relative evaluation subgroup G^rel_n (A, B; 𝜙) of 𝜙 are generated by single elements.
https://doi.org/10.4134/CKMS.c200339 인용 PDF KSCI