Configuration space integral for long n–knots and the Alexander polynomial
Configuration space integral for long n–knots and the Alexander polynomial
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长 n 结和亚历山大多项式的配置空间积分
DOI：
10.2140/agt.2007.7.47
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发表时间：
2007
影响因子：
0.7
通讯作者：
Tadayuki Watanabe
中科院分区：
文献类型：
--
作者：
Tadayuki Watanabe
摄动chen - simons理论有一个高维的类比，在某种意义上，类似于三维的摄动级数，通过位形空间积分计算，产生高维结的不变量（Bott - Cattaneo-Rossi不变量）。这个不变量是由博特为2次构造的，由卡塔内奥-罗西为更高次构造的。然而，它的特征尚不清楚。本文将bot - cattaneo - rossi不变量限定为Habiro - kanenbu - shima[10]引入的长带n -结的有限型不变量。因此，我们得到了用Alexander多项式表示的bot - cattaneo - rossi不变量的非平凡描述。
There is a higher dimensional analogue of the perturbative Chern–Simons theory in the sense that a similar perturbative series as in 3 dimensions, which is computed via configuration space integral, yields an invariant of higher dimensional knots (Bott– Cattaneo–Rossi invariant). This invariant was constructed by Bott for degree 2 and by Cattaneo–Rossi for higher degrees. However, its feature is yet unknown. In this paper we restrict the study to long ribbon n–knots and characterize the Bott–Cattaneo–Rossi invariant as a finite type invariant of long ribbon n–knots introduced by Habiro– Kanenobu–Shima [10]. As a consequence, we obtain a nontrivial description of the Bott–Cattaneo–Rossi invariant in terms of the Alexander polynomial.