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We study the formality of the total space of principal SU(2) and SO(3)-bundles over a Wolf space, that is a symmetric positive quaternionic Kähler manifold. We apply this to conclude that all the 3-Sasakian homogeneous spaces are formal. We also determine the principal SU(2) and SO(3)-bundles over the Wolf spaces whose total space is non-formal.
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Marisa Fernández, Vicente Muñoz, Jonatan Sánchez, On SO(3)-bundles over the Wolf spaces. Rev. Mat. Iberoam. 36 (2020), no. 1, pp. 159–193DOI 10.4171/RMI/1124