On topological Blaschke conjecture. II: Nonexistence of Blaschke structure on fake quaternion projective planes
type: Item
instance of: scholarly article
title: On topological Blaschke conjecture. II: Nonexistence of Blaschke structure on fake quaternion projective planes
zbMATH Open document ID: 0557.53024
author: Hajime Sato
author: Tadayoshi Mizutani
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1984-01-01T00:00:00Z
review text: [For the entire collection see Zbl 0535.00016.] The authors prove that a Blaschke manifold with the integral cohomology ring of \({\mathbb{H}}P^ 2\) is PL-homeomorphic to \({\mathbb{H}}P^ 2\). \textit{H. Gluck}, \textit{F. Warner} and \textit{C. T. Yang} [Duke Math. J. 50, 1041-1076 (1983; Zbl 0534.53039)] proved the same for \({\mathbb{H}}P^ 2\) and \(CaP^ 2\) by somewhat different methods. [For part I see the preceding review.]
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 3888462
zbMATH Keywords: quaternion projective planes
zbMATH Keywords: Blaschke manifold
reviewed by: Gudlaugur Thorbergsson
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178228844
OpenAlex ID: W2045728600
Wikidata QID: Q123015645
cites work: Propriétés globales des espaces de Riemann harmoniques
cites work: Q4169382
cites work: Manifolds which are like projective planes
cites work: Characteristic Classes. (AM-76)
cites work: Q4771357
cites work: On the Structure of Manifolds
cites work: On Pontrjagin classes and homotopy types of manifolds
cites work: 8-manifolds admitting no differentiable structure
cites work: Remarks on differentiable structures on spheres
cites work: Division algebras, fibrations of spheres by great spheres and the topological determination of space by the gross behavior of its geodesics
DOI: 10.2748/TMJ/1178228844
description: scientific article; zbMATH DE number 3888462