16-dimensional compact projective planes with a collineation group of dimension \(\geq 35\) (Q2481719)

Let \({\mathcal P}\) be a topological projective plane with compact \(16\)-dimensional point set, such that the group of continuous collineations of \({\mathcal P}\) contains a connected subgroup \(\Delta\) whose dimension is at least \(35\). Planes where \(\Delta\) does not fix exactly one point and one line have been completely determined [cf. \textit{H. Hähl} and \textit{H. Salzmann}, Arch. Math. 85, 89--100 (2005; Zbl 1077.51003)]. The author examines planes where \(\Delta\) fixes exactly one nonincident point-line pair \((a,W)\). He shows that in this case either the group \(\Delta\) contains \(\text{Spin}_9({\mathbb R}, r)\) for some \(r\leq 1\) and \(\dim\Delta\leq 37\), or \(\dim\Delta\geq 38\), \(\Delta\) acts triply transitive on \(W\) and \(\mathcal P\) is the classical Moufang plane. The proof relies on the stiffness theorem by \textit{R. Bödi} [Geom. Dedicata 53, 201--216 (1994; Zbl 0829.51007)].