nLab 5-manifold

Idea

A manifold of dimension 5

Examples

• 5-sphere

• Wu manifold

Related concepts

• Sasakian manifold, SU(2)-structure

manifolds in low dimension:

• 2-manifolds

• 3-manifolds

• 4-manifolds

• 5-manifolds

• 6-manifolds

• 7-manifolds

• 8-manifolds

• 9-manifolds

• 10-manifolds

• 11-manifolds

• 12-manifolds

• 13-manifolds

• 14-manifolds

• 15-manifolds

• 16-manifolds

References

• Martin Čadek, Jiří Vanžura, On the classification of oriented vector bundles over 5-complexes, Czechoslovak Mathematical Journal, Vol. 43 (1993), No. 4, 753–764 (dml:128427)

On Cohomotopy sets of 5-manifolds:

• Panagiotis Konstantis: Vector bundles and cohomotopies of spin 5-manifolds, Homology, Homotopy and Applications 23 1 (2021) [arXiv:1812.06547, doi:10.4310/HHA.2021.v23.n1.a9]

  (in relation to quaternionic line bundles)

• Steven Amelotte, Tyrone Cutler, Tseleung So: Suspension splittings of 5-dimensional Poincaré duality complexes and their applications, Algebr. Geom. Topol. 26 (2026) 283–319 [doi:10.2140/agt.2026.26.283, arXiv:2311.16073]

• Pengcheng Li, Zhongjian Zhu: The homotopy decomposition of the suspension of a non-simply-connected 5-manifold, Proceedings of the Royal Society of Edinburgh Section A: Mathematics 156 1 (2026) 93–121 [doi:10.1017/prm.2024.49, arXiv:2311.16642]