A note on the rational homotopy type of the projectivization of the tangent bundle of complex projective spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911088909484032 |
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| author | Ndlovu, Meshach Gatsinzi, Jean Baptiste |
| author_facet | Ndlovu, Meshach Gatsinzi, Jean Baptiste |
| contents | In this paper, we determine the rational homotopy type of the total space of the projectivization of the complex tangent bundle $τ: \mathbb{C}^n \longrightarrow E \longrightarrow \mathbb{C}P^{n}$. We show that the total space $P(E)$ of the projectivization bundle $P(τ): \mathbb{C}P^{n-1} \longrightarrow P(E) \longrightarrow \mathbb{C}P^{n}$ has the rational homotopy type of $\mathrm{U}(n+1)/\mathrm{U}(1)\times \mathrm{U}(1)\times \mathrm{U}(n-1)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_01797 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A note on the rational homotopy type of the projectivization of the tangent bundle of complex projective spaces Ndlovu, Meshach Gatsinzi, Jean Baptiste Algebraic Topology Rings and Algebras 55P62, 55P15 In this paper, we determine the rational homotopy type of the total space of the projectivization of the complex tangent bundle $τ: \mathbb{C}^n \longrightarrow E \longrightarrow \mathbb{C}P^{n}$. We show that the total space $P(E)$ of the projectivization bundle $P(τ): \mathbb{C}P^{n-1} \longrightarrow P(E) \longrightarrow \mathbb{C}P^{n}$ has the rational homotopy type of $\mathrm{U}(n+1)/\mathrm{U}(1)\times \mathrm{U}(1)\times \mathrm{U}(n-1)$. |
| title | A note on the rational homotopy type of the projectivization of the tangent bundle of complex projective spaces |
| topic | Algebraic Topology Rings and Algebras 55P62, 55P15 |
| url | https://arxiv.org/abs/2508.01797 |