论文标题
$ \ mathfrak {gl}（1 \ vert 1）$ - 亚历山大多项式$ 3 $ -MANIFOLDS
$\mathfrak{gl}(1 \vert 1)$-Alexander polynomial for $3$-manifolds
论文作者
论文摘要
作为Reshetikhin和Turaev的不变性的扩展，Costantino，Geer和Patureau-Mirand在相对$ G $ - 模块化类别的环境中建造了$ 3 $ manifold不变性，其中包括半味和非隔离的含量和非隔离式纤维碳tensor类别作为示例。在本文中，我们遵循他们的方法来构建Viro的$ \ Mathfrak {gl}（1 \ vert 1）$ - 亚历山大多项式的$ 3 $ manifold不变。我们以镜头空间$ l（7，1）$和$ L（7，2）$作为示例，以表明这种不变的可以区分同性恋歧管。
As an extension of Reshetikhin and Turaev's invariant, Costantino, Geer and Patureau-Mirand constructed $3$-manifold invariants in the setting of relative $G$-modular categories, which include both semisimple and non-semisimple ribbon tensor categories as examples. In this paper, we follow their method to construct a $3$-manifold invariant from Viro's $\mathfrak{gl}(1\vert 1)$-Alexander polynomial. We take lens spaces $L(7, 1)$ and $L(7, 2)$ as examples to show that this invariant can distinguish homotopy equivalent manifolds.
