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A note on the topology and geometry of \(F_4I\). (English) Zbl 1229.57032

Let \(\displaystyle{F_{4}I=\frac{F_{4}}{Sp(3)Sp(1)}}\) be the 28-dimensional quaternion-Kähler manifold, see J. A. Wolf [J. Math. Mech. 14, 1033–1047 (1965; Zbl 0141.38202)]. In this paper the authors compute the intersection pairings of the relevant characteristic classes arising from the quaternion-Kähler structure of \(F_{4}I\), they determine the ring structure of \(H^{*}(F_{4}I;\; \mathbb{Q})\) and give explicitly the Pontrjagin classes and numbers of \(F_{4}I\).

MSC:

57T15 Homology and cohomology of homogeneous spaces of Lie groups
53C26 Hyper-Kähler and quaternionic Kähler geometry, “special” geometry
53C35 Differential geometry of symmetric spaces

Citations:

Zbl 0141.38202
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