DOI: 10.1007/s00454-018-00055-w URL: Authors: D. Gorodkov Journal/publisher: Year: 2019
Title: A 15-Vertex triangulation of the quaternionic projective plane
Abstract: In 1992, Brehm and Kühnel constructed an 8-dimensional simplicial complex M158 with 15 vertices as a candidate to be a minimal triangulation of the quaternionic projective plane. They managed to prove that it is a manifold “like a projective plane” in the sense of Eells and Kuiper. However, it was not known until now if this complex is PL homeomorphic (or at least homeomorphic) to HP2. This problem was reduced to the computation of the first rational Pontryagin class of this combinatorial manifold. Realizing an algorithm due to Gaifullin, we compute the first Pontryagin class of M158. As a result, we obtain that it is indeed a minimal triangulation of HP2.