论文标题
$ 4 $ pundust的球体和$ 1 $ pundust的圆环的绞线代数的强积极性
Strong positivity for the skein algebras of the $4$-punctured sphere and of the $1$-punctured torus
论文作者
论文摘要
Kauffman支架绞线代数是对$ sl_2 $ the拓扑表面的$ sl_2 $字符的定期功能代数的量化。我们意识到$ 4 $命令的球体的绞线代数是基于较高属的gromov-witten理论的镜像对称性结构的输出，并应用于复杂的立方表面。使用此结果，我们证明了$ 4 $ undust的球体和$ 1 $ cunctund的圆环的手镯基础的结构常数的阳性。 $ 4 $启用的球体的拓扑与立方表面曲线的枚举几何形状之间的这种联系是数学表现出来的数学表现，是$ \ Mathcal {n} = 2 $ $ $ $ n_f = 4 $ $ su（2）$ su（2）$测定理论，在字符串/M理论中存在双重描述。
The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on the $SL_2$ character variety of a topological surface. We realize the skein algebra of the $4$-punctured sphere as the output of a mirror symmetry construction based on higher genus Gromov-Witten theory and applied to a complex cubic surface. Using this result, we prove the positivity of the structure constants of the bracelets basis for the skein algebras of the $4$-punctured sphere and of the $1$-punctured torus. This connection between topology of the $4$-punctured sphere and enumerative geometry of curves in cubic surfaces is a mathematical manifestation of the existence of dual descriptions in string/M-theory for the $\mathcal{N}=2$ $N_f=4$ $SU(2)$ gauge theory.
