Equilibrium triangulations of the complex projective plane
The equilibrium set of \(CP^ 2\) in its standard representation is the torus \(| x| = | y | = | z |\). An equilibrium triangulation of \(CP^ 2\) includes a triangulation of this torus, which has at least 7 vertices. So the simplest equilibrium triangulation has 10 vertices. Similar triangulations with more vertices are explicitly given together with their automorphism groups. As a corollary the authors give a prove of the Kuiper-Massey theorem: Modulo conjugation, \(CP^ 2\) is \(PL\)-homeomorphic to \(S^ 4\). Tight embeddings are given for the 10- vertices triangulation and its real analogue.
scientific article; zbMATH DE number 147305