论文标题
a-polynomials，托勒密方程和dehn填充
A-polynomials, Ptolemy equations and Dehn filling
论文作者
论文摘要
A-Polynomial编码结和相关歧管上的双曲几何信息。从历史上看，很难计算，并且特别困难地确定无限的结族的a多项式。在这里，我们通过从歧管的三角剖分开始，然后使用编码编码粘合物的Neumann-Zagier矩阵的符号性能来计算A-Polynomials，以更改计算的基础。结果是简化定义方程式。我们将此方法应用于Dehn Filling获得的流形家族，并表明其A-Polynomials的定义方程是托勒密方程，最多可以符号，直到符号为Cusp圆环群集代数中的群集变量之间的方程。
The A-polynomial encodes hyperbolic geometric information on knots and related manifolds. Historically, it has been difficult to compute, and particularly difficult to determine A-polynomials of infinite families of knots. Here, we compute A-polynomials by starting with a triangulation of a manifold, then using symplectic properties of the Neumann-Zagier matrix encoding the gluings to change the basis of the computation. The result is a simplification of the defining equations. We apply this method to families of manifolds obtained by Dehn filling, and show that the defining equations of their A-polynomials are Ptolemy equations which, up to signs, are equations between cluster variables in the cluster algebra of the cusp torus.
