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

2025/08/05 by Ndlovu, Meshach
#55P62 #Algebraic Topology (math.AT) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.03871

Abstract

In this paper, we compute the rational homotopy type of the quaternionic projective bundle P(τ): ℍP^n-1 → P(E) → M obtain from the quaternionic tangent bundle τ: ℍⁿ → E → M over quaternionic manifold M. If the base space M is the quaternionic projective space ℍP², 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) × Sp(1).

Citations

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

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