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• W3194761358 abstract "Kashaev and Reshetikhin previously described a way to define holonomy invariants of knots using quantum $mathfrak{sl}_2$ at a root of unity. These are generalized quantum invariants depend both on a knot $K$ and a representation of the fundamental group of its complement into $mathrm{SL}_2(mathbb{C})$; equivalently, we can think of $mathrm{KR}(K)$ as associating to each knot a function on (a slight generalization of) its character variety. In this paper we clarify some details of their construction. In particular, we show that for $K$ a hyperbolic knot $mathrm{KaRe}(K)$ can be viewed as a function on the geometric component of the $A$-polynomial curve of $K$. We compute some examples at a third root of unity." @default.
• W3194761358 created "2021-08-30" @default.
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• W3194761358 date "2021-08-14" @default.
• W3194761358 modified "2023-09-26" @default.
• W3194761358 title "Kashaev--Reshetikhin Invariants of Links" @default.
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• W3194761358 doi "https://doi.org/10.48550/arxiv.2108.06561" @default.
• W3194761358 hasPublicationYear "2021" @default.
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