On SO(3)-bundles over the Wolf spaces
Marisa Fern\'andez, Jonatan S\'anchez, Vicente Mu\~noz
TL;DR
This paper investigates the formality properties of total spaces of principal SU(2) and SO(3) bundles over Wolf spaces, concluding that all 3-Sasakian homogeneous spaces are formal and identifying non-formal cases.
Contribution
It provides a classification of formality for bundles over Wolf spaces and establishes the formality of all 3-Sasakian homogeneous spaces.
Findings
All 3-Sasakian homogeneous spaces are formal.
Identifies principal bundles over Wolf spaces with non-formal total spaces.
Classifies cases where total space is non-formal.
Abstract
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 K\"ahker 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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