Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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Evaluation Subgroups of Mapping Spaces over Grassmann Manifolds

  • Abdelhadi Zaim (Department of Mathematics and Computer Sciences, Faculty of Sciences Ain Chock, University Hassan II)
  • Received : 2021.11.13
  • Accepted : 2022.05.09
  • Published : 2023.03.31
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Abstract

Let Vk,n (ℂ) denote the complex Steifel and Grk,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 : 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 Grel* (Grk,k+n (ℂ), Vk,k+n (ℂ) ; p) ⊕ G* (Vk,k+n (ℂ)).

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Acknowledgement

The author is very grateful to the referee for carefully reading the manuscript and his helpful suggestions.

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