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Date
2024-05-13Type
- Working Paper
ETH Bibliography
yes
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Abstract
Determining the structure of the Kauffman bracket skein module of all $3$-manifolds over the ring of Laurent polynomials $\mathbb Z[A^{\pm 1}]$ is a big open problem in skein theory. Very little is known about the skein module of non-prime manifolds over this ring. In this paper, we compute the Kauffman bracket skein module of the $3$-manifold $(S^1 \times S^2) \ \# \ (S^1 \times S^2)$ over the ring $\mathbb Z[A^{\pm 1}]$. We do this by analysing the submodule of handle sliding relations, for which we provide a suitable basis. Along the way we also compute the Kauffman bracket skein module of $(S^1 \times S^2) \ \# \ (S^1 \times D^2)$. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000673473Publication status
publishedJournal / series
arXivPages / Article No.
Publisher
Cornell UniversityEdition / version
v2Subject
Knot theory; Quantum topologyOrganisational unit
02889 - ETH Institut für Theoretische Studien / ETH Institute for Theoretical Studies
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ETH Bibliography
yes
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