An effective proof of finiteness for Kauffman bracket skein modules
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866916824391614464 |
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| author | Belletti, Giulio Detcherry, Renaud |
| author_facet | Belletti, Giulio Detcherry, Renaud |
| contents | 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}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_02589 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An effective proof of finiteness for Kauffman bracket skein modules Belletti, Giulio Detcherry, Renaud Geometric Topology 57K31 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}. |
| title | An effective proof of finiteness for Kauffman bracket skein modules |
| topic | Geometric Topology 57K31 |
| url | https://arxiv.org/abs/2507.02589 |