Seminar

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Sol geometry is one of the eight Thurston geometries and provides a natural setting in which geometry, dynamics, and combinatorics interact. In this talk, I will describe a combinatorial approach to understanding Sol 3-manifolds via the notion of being “locally combinatorially defined” (LCD), developed in joint work with D. Cooper and L. Mavrakis. I will explain how symbolic methods—particularly regular languages—are used to construct a branched 3-manifold encoding the local structure of Sol geometry, and how this construction shows that Sol 3-manifolds are LCD. This perspective yields a characterization of Sol manifolds in terms of local combinatorial data and highlights a connection between 3-manifold geometry and formal language theory.