A Combinatorial Characterization of Sol 3-Manifolds
arXiv:2606.23963
Abstract
We show that there is a universal compact branched 3-manifold such that a closed 3-manifold immerses into if and only if 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 is based on a regular language that characterizes Sol manifolds.
20 pages, 2 figures