A Combinatorial Characterization of Sol 3-Manifolds

Daryl Cooper; Leslie Mavrakis; Priyam Patel

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arXiv · 2606.23963

A Combinatorial Characterization of Sol 3-Manifolds

Daryl Cooper·Leslie Mavrakis·Priyam Patel

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Abstract

We show that there is a universal compact branched 3-manifold $W$ such that a closed 3-manifold $M$ immerses into $W$ if and only if $M$ admits a Sol structure. Equivalently, a closed 3-manifold is Sol if and only if it has a certain type of triangulation. The construction of $W$ is based on a regular language that characterizes Sol manifolds.

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Daryl Cooper, Leslie Mavrakis, Priyam Patel. 2026-06-22. A Combinatorial Characterization of Sol 3-Manifolds. https://arxiv.org/abs/2606.23963

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