A note on the rational homotopy type of the projectivization of the tangent bundle of complex projective spaces

2025/08/03 by Meshach Ndlovu, Ndlovu, Meshach, J.-B. Gatsinzi +1 · 1 citation
Mathematics · #55P15 #55P62 #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2508.01797

openalex publication_date 2025/08/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we determine the rational homotopy type of the total space of the projectivization of the complex tangent bundle τ: ℂⁿ \longrightarrow E \longrightarrow ℂPⁿ. We show that the total space P(E) of the projectivization bundle P(τ): ℂP^n-1 \longrightarrow P(E) \longrightarrow ℂPⁿ has the rational homotopy type of U(n+1)/U(1)× U(1)× U(n-1).

Citations

• Poincare duality and commutative differential graded algebras

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• The biquotient model of the total space of the projectivization quaternionic bundles over certain manifolds

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