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This is a Quantitative Study study.

Finiteness and Dimension of Stated Skein Modules over Frobenius

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This analysis demonstrates finite-dimensional properties in skein modules, indicating compact structures in 3-manifolds.

The stated skein module is finitely generated over certain parameters, indicating structural properties.
An upper bound for the dimension of the skein module is provided when considering compact marked 3-manifolds.
The research reveals that the skein module captures important characteristics of punctured bordered surfaces.
The dimension of the module is closely tied to the boundary components and Euler characteristics of the surfaces considered.

Zhihao Wang (2025) studied this question.

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