Herrera, Rafael; Nagatomo, Yasuyuki A note on the topology and geometry of \(F_4I\). (English) Zbl 1229.57032 Rend. Mat. Appl., VII. Ser. 30, No. 2, 183-193 (2010). 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 \(F_{4}I\). Reviewer: Saïd Zarati (Tunis) 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 Keywords:symmetric space; quaternion-Kähler manifold; cohomology ring; intersection number Citations:Zbl 0141.38202 PDFBibTeX XMLCite \textit{R. Herrera} and \textit{Y. Nagatomo}, Rend. Mat. Appl., VII. Ser. 30, No. 2, 183--193 (2010; Zbl 1229.57032)