Presentations of Kauffman bracket skein algebras of planar surfaces

Abstract

Let $R$ be a commutative ring with identity and a fixed invertible element $q^{\frac{1}{2}}$, and suppose $q+q^{-1}$ is invertible in $R$. For each planar surface ${\Sigma }_{0,n+1}$, we present its Kauffman bracket skein algebra over $R$ by explicit generators and relations. The presentation is independent of $R$, and can be considered as a quantization of the trace algebra of $n$ generic $2\times 2$ unimodular matrices.

22 pages, 12 figures. The original paper arXiv:2206.07856 has been separated into two parts. This is the second part