New examples of compact 8-manifolds of holonomy Spin(7)
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 \(b^3=0\).
scientific article; zbMATH DE number 1489532