$\mathbb{S}ol^3\times\mathbb{E}^1$-manifolds

J. A. Hillman

doi:10.1017/S14467887000258

$\mathbb{S}ol^3\times\mathbb{E}^1$-manifolds

Geometric Topology 2021-02-24 v3 Differential Geometry

Authors: J. A. Hillman

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Abstract

We show that $\mathbb{S}ol^3\times\mathbb{E}^1$ -manifolds are Seifert fibred, with general fibre the torus, and base one of the seven 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 a classification of such 4-manifolds.

Keywords

manifolds

Cite

@article{arxiv.1304.2436,
  title  = {$\mathbb{S}ol^3\times\mathbb{E}^1$-manifolds},
  author = {J. A. Hillman},
  journal= {arXiv preprint arXiv:1304.2436},
  year   = {2021}
}

Comments

The earlier version (2013) was fatally flawed. The present version retains only the focus on Seifert fibration as a basis for classification

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