Equilibrium triangulations of the complex projective plane
type: Item
instance of: scholarly article
title: Equilibrium triangulations of the complex projective plane
zbMATH Open document ID: 0769.52013
DOI: 10.1007/BF00181398
author: Wolfgang Kühnel
author: Tom Banchoff
published in: Geometriae Dedicata
publication date: 1993-04-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 52B70
Mathematics Subject Classification ID: 57Q15
Mathematics Subject Classification ID: 57Q25
zbMATH DE Number: 147305
zbMATH Keywords: complex projective plane
zbMATH Keywords: tight embeddings
zbMATH Keywords: equilibrium triangulation
zbMATH Keywords: automorphism groups
zbMATH Keywords: Kuiper-Massey theorem
reviewed by: Erhard Heil
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf00181398
OpenAlex ID: W2062697604
description: scientific article; zbMATH DE number 147305