U_q（sl_2）-表示的拓扑描述

On Hopf-induced deformation of topological locus

We provide a very brief review of the description of colored invariants for the Hopf link in terms of characters, which need to be taken at a peculiar deformation of the topological locus, depending on one of the two representations associated with the two components of the link. Most important, we extend the description of this locus to conjugate and, generically, to composite representations and also define the "adjoint" Schur functions emerging in the dual description.

2-表示与等变二维拓扑域论

2-Representations and Equivariant 2D Topological Field Theories

根据G. Moore和G. Segal，我们从任意Frobenius代数中明确构造了G-等变拓扑域论，该代数具有有限群G的扭曲作用。

Topological formula of the loop expansion of the colored Jones polynomials

We give a topological formula of the loop expansion of the colored Jones polynomials by using identification of generic quantum sl2 representation with homological representations. This gives a direct topological proof of the Melvin-Morton-Rozansky conjecture, and a connection between entropy of braids and quantum representations.

环面上$U_q(sl_2)$的拓扑表示及映射类群

Topological Representations of $U_q(sl_2)$ on the Torus and the Mapping Class Group

我们计算映射类群作用于环上的配置空间的一个穿刺，在共形场论中产生的局部系统中的系数。这个作用与量子群$U_q(sl_2)$的拓扑作用是交换的，并且以顶点形式给出。

Knizhnik-Zamolodchikov丛是拓扑平凡的

Knizhnik-Zamolodchikov bundles are topologically trivial

证明了Knizhnik-Zamolodchikov表示和辫群表示的量子结构的核上的向量丛是拓扑平凡丛.我们将这个结果部分推广到广义辫群。一个重要的中间结果是，n个字母上的对称群的表示环是由其自然n维表示的交替幂生成的。

表示论、拓扑场论和安德鲁斯-柯蒂斯猜想

Representation theory, topological field theory, and the Andrews-Curtis conjecture

我们提出了一个代表性理论的问题，试图解决的Andrews-Curtis猜想。粗略地说，是否存在一个具有自对偶不可约表示$V_i$的集合的三角Hopf代数，使得任意两个表示的乘积分解为$V_i$和$\sum (\rank V_i)^2=0$的副本之和？这些数据可以用来构建一个“拓扑量子场论”的2-复合物，这是一个很好的机会检测反例的猜想。