text: 23,54,1429482848495546372,1291064871510069249,Calvin McPhail-Snyder,"New paper up on the arXiv! I'm a bit belated tweeting about it because I was at the lake last week when it went up <LINK> This paper works out the details of a construction of Kashaev and Reshetikhin. The idea is to improve ordinary quantum invariants of topological objects by ""twisting"" them with geometric data, in this case, reps of π_1 into SL_2(C) My thesis was on a similar construction, which has considerably more technical issues. This paper is nice because we can avoid them and do some explicit, algebraic computations. I am hopeful that this sort of thing will provide useful for geometric topology, especially hyperbolic knot theory. If you're interested in doing this sort of thing, please let me know!",https://arxiv.org/abs/2108.06561,"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. ",Kashaev--Reshetikhin Invariants of Links,4,"[""New paper up on the arXiv! I'm a bit belated tweeting about it because I was at the lake last week when it went up <LINK>"", 'This paper works out the details of a construction of Kashaev and Reshetikhin. The idea is to improve ordinary quantum invariants of topological objects by ""twisting"" them with geometric data, in this case, reps of π_1 into SL_2(C)', 'My thesis was on a similar construction, which has considerably more technical issues. This paper is nice because we can avoid them and do some explicit, algebraic computations.', ""I am hopeful that this sort of thing will provide useful for geometric topology, especially hyperbolic knot theory. If you're interested in doing this sort of thing, please let me know!""]",21,08,717