The biquotient model of the total space of the projectivization quaternionic bundles over certain manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912522014031872 |
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| author | Ndlovu, Meshach |
| author_facet | Ndlovu, Meshach |
| contents | In this paper, we compute the rational homotopy type of the quaternionic projective bundle $P(τ): \mathbb{H}P^{n-1} \rightarrow P(E) \rightarrow M$ obtain from the quaternionic tangent bundle $τ: \mathbb{H}^{n} \rightarrow E \rightarrow M$ over quaternionic manifold $M$. If the base space $M$ is the quaternionic projective space $\mathbb{H}P^{2}$, then the rational homotopy type of the total space $P(E)$ of the quaternionic projective bundle $P(τ)$ is given by a biquotient model $Sp(1)\backslash Sp(3) / Sp(1) \times Sp(1)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_03871 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The biquotient model of the total space of the projectivization quaternionic bundles over certain manifolds Ndlovu, Meshach Algebraic Topology 55P62 In this paper, we compute the rational homotopy type of the quaternionic projective bundle $P(τ): \mathbb{H}P^{n-1} \rightarrow P(E) \rightarrow M$ obtain from the quaternionic tangent bundle $τ: \mathbb{H}^{n} \rightarrow E \rightarrow M$ over quaternionic manifold $M$. If the base space $M$ is the quaternionic projective space $\mathbb{H}P^{2}$, then the rational homotopy type of the total space $P(E)$ of the quaternionic projective bundle $P(τ)$ is given by a biquotient model $Sp(1)\backslash Sp(3) / Sp(1) \times Sp(1)$. |
| title | The biquotient model of the total space of the projectivization quaternionic bundles over certain manifolds |
| topic | Algebraic Topology 55P62 |
| url | https://arxiv.org/abs/2508.03871 |