Yokota type invariants derived from non-integral highest weight representations of $U_q(sl_2)$

关于各种量子不变量渐近展开的研究 III：沿扭转结做整系数手术所得的闭双曲 3-流形的 Reshetikhin-Turaev 不变量

On the asymptotic expansion of various quantum invariants III: the Reshetikhin-Turaev invariants of closed hyperbolic 3-manifolds obtained by doing integral surgery along the twist knot

本文利用 Ohtsuki-Yokota 鞍点方法，给出了沿扭转结做整系数 q-手术所得闭双曲 3-流形在单位根处的 Reshetikhin-Turaev 不变量的渐近展开公式。

A homological model for $U_q \mathfrak{sl}(2)$ Verma-modules and their braid representations

We extend Lawrence's representations of the braid groups to relative homology modules, and we show that they are free modules over a Laurent polynomials ring. We define homological operators and we show that they actually provide a representation for an integral version for $U_q \mathfrak{sl}(2)$. We suggest an isomorphism between a given basis of homological modules and the standard basis of tensor products of Verma modules, and we show it to preserve the integral ring of coefficients, the action of $U_q \mathfrak{sl}(2)$, the braid group representations and their grading. This recovers an in…