Skein modules and character varieties of Seifert manifolds

We show that the Kauffman bracket skein module of a closed Seifert fibered 3-manifold M M is finitely generated over Z [ A ± 1 ] Z[A± 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)| .