The Kauffman bracket skein module of \(S^ 1\times S^ 2\)
We compute the skein module \({\mathcal S} (S^1\times S^2)\). This module over the ring \(R= \mathbb{Z} [A^{\pm 1}]\) generalizes the Jones polynomial to links in \(S^1\times S^2\). The definition of \({\mathcal S} (S^1\times S^2)\) rests squarely on Kauffman's approach to the Jones polynomial via his bracket polynomial. In particular we obtain Theorem: The skein module of \(S^1\times S^2\) is \[ {\mathcal S} (S^1\times S^2) \cong R\oplus \bigoplus ^\infty_{i=1} R/(1- A^{2i+4}). \]
skein module \({\mathcal S} (S^ 1\times S^ 2)\)
scientific article; zbMATH DE number 799548