New examples of compact 8-manifolds of holonomy Spin(7)
type: Item
instance of: scholarly article
title: New examples of compact 8-manifolds of holonomy Spin(7)
zbMATH Open document ID: 0961.53024
author: Christine Taylor
published in: Mathematical Research Letters
publication date: 2000-08-13T00:00:00Z
review text: D. Joyce constructed compact manifolds with Spin(7) holonomy by resolving \(T^8/G\), where \(G=\mathbb{Z}^4_2\) or \(\mathbb{Z}^5_2\) acts on \(T^8\) preserving the 4-form which defines the Spin(7)-structure [\textit{D. D. Joyce}, Invent. Math. 123, No. 3, 507-552 (1996; Zbl 0858.53037)]. The 3rd Betti number of these manifolds is 16, 8 or 4. In the present paper this construction is extended by considering the action of \(G=\mathbb{Z}^6_2\) (adding one additional generator to the group \(\mathbb{Z}^5_2\) considered by Joyce) and resolving the singularities. The author finds 28 new examples of compact manifolds with holonomy Spin(7) and \(b^3=0\).
reviewed by: Helga Baum
Mathematics Subject Classification ID: 53C29
Mathematics Subject Classification ID: 53C27
zbMATH DE Number: 1489532
zbMATH Keywords: special holonomy
zbMATH Keywords: Spin(7) holonomy
MaRDI profile type: Publication
full work available at URL: mrl.1999.v6.n5.a8
OpenAlex ID: W2334068303
DOI: 10.4310/MRL.1999.V6.N5.A8
description: scientific article; zbMATH DE number 1489532