论文标题
扭曲的Kuperberg结的kuperberg结和Reidemeister Torsion通过扭曲的Drinfeld双打
Twisted Kuperberg invariants of knots and Reidemeister torsion via twisted Drinfeld doubles
论文作者
论文摘要
在本文中，我们考虑了从Hopf代数的扭曲的drinfeld双人双球中获得的三个球的reshetikhin-turaev不变的，或者等效地，交叉产品的相对Drinfeld中心$ \ text {rep} {rep}（pep}（h）\ rtimes \ rtimes \ rtimes \ text \ text {aut} aut {aut}（h）$。这些是结的量子不变性，并具有结组的同构为$ \ text {aut}（h）$。我们表明，至少对于三个球体的结，这些不变式提供了对福克斯 - 卡尔库鲁斯串行的kuperberg不变式的无关紧要的概括，作者先前引入的sutured歧管，仅针对参与性的Hopf代数定义。特别是，我们描述了$ sl（n，\ mathbb {c}）$ - 扭曲的reidemister torsion torsion torsion作为reshetikhin-turaev不变。
In this paper, we consider the Reshetikhin-Turaev invariants of knots in the three-sphere obtained from a twisted Drinfeld double of a Hopf algebra, or equivalently, the relative Drinfeld center of the crossed product $\text{Rep}(H)\rtimes\text{Aut}(H)$. These are quantum invariants of knots endowed with a homomorphism of the knot group to $\text{Aut}(H)$. We show that, at least for knots in the three-sphere, these invariants provide a non-involutory generalization of the Fox-calculus-twisted Kuperberg invariants of sutured manifolds introduced previously by the author, which are only defined for involutory Hopf algebras. In particular, we describe the $SL(n,\mathbb{C})$-twisted Reidemeister torsion of a knot complement as a Reshetikhin-Turaev invariant.
