An effective proof of finiteness for Kauffman bracket skein modules

Giulio Belletti; Renaud Detcherry

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arXiv · 2507.02589

An effective proof of finiteness for Kauffman bracket skein modules

Giulio Belletti·Renaud Detcherry

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Abstract

We prove a version of the finiteness conjecture for Kauffman bracket skein modules of $3$-manifolds with boundary, which was introduced by the second author in \cite{Det21}. In particular our methods, which are constructive, give an alternative proof of Witten's finiteness conjecture for the Kauffman bracket skein modules of closed $3$-manifolds, which was originally proved in \cite{GJS19}. Moreover, as a corollary we show that the peripheral ideal of any link is non-empty, answering a question of Frohman, Gelca and Lofaro \cite{FGL02}.

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Giulio Belletti, Renaud Detcherry. 2025-07-03. An effective proof of finiteness for Kauffman bracket skein modules. https://arxiv.org/abs/2507.02589

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