$\mathbb{S}\text{ol}^{3}\times \mathbb{E}^{1}$-MANIFOLDS. (4th December 2017)

• Record Type: Journal Article
• Authors: HILLMAN, J. A.
• Is Part Of: Journal of the Australian Mathematical Society. Volume 105:Number 1(2018)
• Page Start: 46
• Page End: 56
• Publication Date: 2017-12-04
• Subjects: primary 57M50, -- secondary 53C30; lattice, -- 4-manifold, -- Seifert fibration, -- solvable Lie group, -- Sol3 ×E1; Mathematics -- Periodicals; Statistics -- Periodicals; Mathematical statistics -- Periodicals; 510.5
• DOI: 10.1017/S1446788717000258
• Languages: English
• ISSNs: 1446-7887

Abstract

Abstract : We show that closed $\mathbb{S}\text{ol}^{3}\times \mathbb{E}^{1}$ -manifolds are Seifert fibred, with general fibre the torus, and base one of the flat 2-orbifolds $T, Kb, \mathbb{A}, \mathbb{M}b, S(2, 2, 2, 2), P(2, 2)$ or $\mathbb{D}(2, 2)$, and outline how such manifolds may be classified.