SU(2)-bundles over highly connected 8-manifolds

2024/05/21 by Samik Basu, Basu, Samik, Aloke Kr. Ghosh +3
Mathematics · #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2405.12835

Abstract

In this paper, we analyze the possible homotopy types of the total space of a principal SU(2)-bundle over a 3-connected 8-dimensional Poincaré duality complex. Along the way, we also classify the 3-connected 11-dimensional complexes E formed from a wedge of S⁴ and S⁷ by attaching a 11-cell.

Related

• Manifold structures on highly connected Poincaré complexes
• Manifolds with an SU(2)-action on the tangent bundle
• Eight-dimensional SU(3)-manifolds of cohomogeneity one
• On the mapping class groups of ℙ¹-bundles over ℙ²
• On 1-connected 8-manifolds with the same homology as S³× S⁵