论文标题
简单theta曲线和对称图的决定因素
Determinants of Simple Theta Curves and Symmetric Graphs
论文作者
论文摘要
theta曲线是三个球体中$θ$ graph的空间嵌入，占环境同位素。我们将theta曲线的决定因素定义为源自其klein覆盖物的第一个同源性引起的整数值。当theta曲线很简单，包含一个组成的解管时，我们证明theta曲线的决定因素是组成结的决定因素的乘积。我们的证明是组合的，依赖于Kirchhoff的矩阵树定理以及对称，签名的平面图的跨越树枚举结果。
A theta curve is a spatial embedding of the $θ$-graph in the three-sphere, taken up to ambient isotopy. We define the determinant of a theta curve as an integer-valued invariant arising from the first homology of its Klein cover. When a theta curve is simple, containing a constituent unknot, we prove that the determinant of the theta curve is the product of the determinants of the constituent knots. Our proofs are combinatorial, relying on Kirchhoff's Matrix Tree Theorem and spanning tree enumeration results for symmetric, signed, planar graphs.
