Abstract—Inspired by Kirby’s work in which constructed the Poincare 3-sphere S^3/2I by an E₈-plumbing, we worked out a general and systematic argument to show that other spherical 3-manifolds S³/2O, S³/2T and S³/2D_n can be obtained from a plumbing construction by the Dynkin diagrams E₇, E₆, and D_n+2, respectively.

Key words—3-Manifolds, vector bundles, Seifert fiber spaces, invariant theory

Yifei Zhao is with Phillips Exeter Academy, Exeter, NH, USA.

Cite:Yifei Zhao, "A Family of 3-Manifolds Arising from the Plumbing Construction," International Journal of Applied Physics and Mathematics vol. 13, no. 4, pp. 62-79, 2023.

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