双曲连杆和调节器的$SL_2(\mathbb{C})$ - Character变体
$SL_2(\mathbb{C})$-Character Variety of a Hyperbolic Link and Regulator
摘要：
本文研究了$S^3$中双曲杆的$SL_2(\mathbb{C})$特征簇。我们分析了一个特殊的光滑射影簇$Y^h$产生的一些1维不可约片的字符簇。我们证明了从这些1维切片得到的自然符号是$K_2({\mathbb C}(Y^h))$中的挠。利用从$K_2$到相应Deligne上同调的调节映射，得到了$Y^h$的某些Zeromki开子集上的变分公式.由此我们对双曲链和纽结的一个可能的参数化体积猜想进行了讨论。
英文摘要：
In this paper, we study the $SL_2(\mathbb{C})$ character variety of a hyperbolic link in $S^3$. We analyze a special smooth projective variety $Y^h$ arising from some 1-dimensional irreducible slices on the character variety. We prove that a natural symbol obtained from these 1-dimensional slices is a torsion in $K_2({\mathbb C}(Y^h))$. By using the regulator map from $K_2$ to the corresponding Deligne cohomology, we get some variation formulae on some Zariski open subset of $Y^h$. From this we give some discussions on a possible parametrized volume conjecture for both hyperbolic links and knots.
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