论文标题
虚拟缠结的绞合理论
Skein theories for virtual tangles
论文作者
论文摘要
在本文中，我们使用Kkein理论技术来对具有某些较小度条件的所有虚拟结多项式和三价不变性分类进行分类。纸的前半部分分类了所有虚拟结多项式的分类，这些多项式具有严格小于Higman-Sims Spin模型的非平凡不变式。特别是，我们展示了一个带有$ \ text {rep}（o（2））$的绞线理论系列。此外，所有针对某些较小条件的定向虚拟缠结理论都被分类。在本文的后半部分，我们将来自对称三价类别的（也许是非平面）三价图形的所有非平凡不变分类进行了分类。对于这些类别中的每个类别，我们还对仅编织三价顶点生成的子类别进行分类。这是一个有趣的示例，来自张量类别Deligne的$ S_T $。
In this paper, we use skein-theoretic techniques to classify all virtual knot polynomials and trivalent graph invariants with certain smallness conditions. The first half of the paper classifies all virtual knot polynomials giving non-trivial invariants strictly smaller than the one given by the Higman-Sims spin model. In particular, we exhibit a family of skein theories coming from $\text{Rep}(O(2))$ with an interesting braiding. In addition, all skein theories of oriented virtual tangles with some smallness conditions are classified. In the second half of the paper, we classify all non-trivial invariants of (perhaps non-planar) trivalent graphs coming from symmetric trivalent categories. For each of these categories, we also classify when the sub-category generated by only the trivalent vertex is braided. An interesting example of this arise from the tensor category Deligne's $S_t$.
