论文标题
从积分到有限类型不变的组合公式 - 案例研究
From integrals to combinatorial formulas of finite type invariants -- a case study
论文作者
论文摘要
我们获得了Casson结的配置空间的局部版本，在该版本中，标准的对称高斯形式被当地支持的形式代替。这里提出的论点与经典论点之间的一个有趣的技术区别在于，在隐藏和异常面孔上消失了积分，不需要众所周知的“互动技巧”。积分公式很容易产生常规结图的众所周知的箭头图表达式，该图首先由Polyak和viro在作品中提出。此外，它产生了多个打结图（例如花瓣图）的箭头图计数，并为{\ em {ü} bercrossing number}提供了新的下限。以前，已知的箭头图公式仅适用于常规结图。
We obtain a localized version of the configuration space integral for the Casson knot invariant, where the standard symmetric Gauss form is replaced with a locally supported form. An interesting technical difference between the arguments presented here and the classical arguments is that the vanishing of integrals over hidden and anomalous faces does not require the well known "involution tricks". The integral formula easily yields the well-known arrow diagram expression for regular knot diagrams, first presented in the work by Polyak and Viro. Moreover, it yields an arrow diagram count for the multicrossing knot diagrams, such as petal diagrams and gives a new lower bound for the {\em {ü}bercrossing number}. Previously, the known arrow diagram formulas were applicable only to the regular knot diagrams.
