论文标题
第四个统一根的三个manifolds的绞线代数
Skein Algebras of Three-Manifolds at 4th Roots of Unity
论文作者
论文摘要
本文介绍了绞线模块的一个代数结构，该链条的$ 3 $ -MANIFOLD $ M $由链接跨度为$ 0 $ in $ H_1中的$ 0 $（M; \ Mathbb {Z} _2）$当使用在Kauffman Bracket Skein相关的参数的价值相等时，事实证明，如果$ m $在$ h_1中没有$ 2 $ - torsion（m; \ m; \ m mathbb {z}）$，那么这些代数，$ k _ {\ pm {\ bf i}}}^0（m）$，自然是对相应的ealgebras nes nes the ealgebras nes the of pm $ $ pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm pm的。这意味着代数$ k _ {\ pm {\ bf i}}}^0（m）$是$ psl_2（\ mathbb {c}）$ - $π_1（m）$的$ psl_2（\ mathbb {c}）$的未还原的坐标环。
This paper introduces an algebra structure on the part of the skein module of an arbitrary $3$-manifold $M$ spanned by links that represent $0$ in $H_1(M;\mathbb{Z}_2)$ when the value of the parameter used in the Kauffman bracket skein relation is equal to $\pm {\bf i}$. It is proved that if $M$ has no $2$-torsion in $H_1(M;\mathbb{Z})$ then those algebras, $K_{\pm {\bf i}}^0(M)$, are naturally isomorphic to the corresponding algebras when the value of the parameter is $\pm 1$. This implies that the algebra $K_{\pm{\bf i}}^0(M)$ is the unreduced coordinate ring of the variety of $PSL_2(\mathbb{C})$-characters of $π_1(M)$ that lift to $SL_2(\mathbb{C})$-representations.
