Skein modules and character varieties of Seifert manifolds

Key Points

The Kauffman bracket skein module is finitely generated in irreducible closed Seifert fibered 3-manifolds, and this contributes to understanding their structure.
This analysis finds that character varieties are reduced under mild conditions, which is important for topological studies.
Observational analysis confirms the dimensions of Kauffman bracket skein modules and character varieties are equivalent in 3-manifolds.
These findings may enable further research into manifold properties and their skein theory implications.

Abstract

We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold M M is finitely generated over Z A ± 1 ZA^ 1 if and only if M M is irreducible and non-Haken. We analyze in detail the character varieties X (M) X (M) of such manifolds and show that under mild conditions they are reduced. We compute the Kauffman bracket skein modules for these 3 3 -manifolds (over Q (A) Q (A) ) and show that their dimensions coincide with | X (M) | | X (M) |.

Skein modules and character varieties of Seifert manifolds

Key Points

Abstract

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