论文标题
$ t^2 \ times i $ with卷猜想行为中的链接的量子不变
A Quantum Invariant of Links in $T^2 \times I$ with Volume Conjecture Behavior
论文作者
论文摘要
我们定义了增厚的圆环中链接的多项式不变$ j_n^t $。我们称$ j^t_n $ $ n $ th toroidal彩色琼斯多项式，并表明它满足了原始有色琼斯多项式的许多属性。最重要的是，$ j_n^t $表现出数量的猜想行为。我们证明了2 by-2平方编织的体积猜想，并为其他链接提供了计算证据。我们还提供了两个等效的构建$ j_n^t $，一个是通用操作员不变的，我们称为伪操作员不变式，另一个使用kauffman支架skein skein模块。最后，我们显示$ j^t_n $产生的双层和虚拟链接不变。据我们所知，$ j^t_n $给出了虚拟（非古典）链接中音量猜想行为的第一个示例。
We define a polynomial invariant $J_n^T$ of links in the thickened torus. We call $J^T_n$ the $n$th toroidal colored Jones polynomial, and show it satisfies many properties of the original colored Jones polynomial. Most significantly, $J_n^T$ exhibits volume conjecture behavior. We prove the volume conjecture for the 2-by-2 square weave, and provide computational evidence for other links. We also give two equivalent constructions of $J_n^T$, one as a generalized operator invariant we call a pseudo-operator invariant, and another using the Kauffman bracket skein module of the torus. Finally, we show $J^T_n$ produces invariants of biperiodic and virtual links. To our knowledge, $J^T_n$ gives the first example of volume conjecture behavior in a virtual (non-classical) link.
