Grope cobordism and feynman diagrams
Grope cobordism and feynman diagrams
复制标题
摸索共边和费曼图
DOI：
--
复制
发表时间：
2002
期刊：
影响因子：
--
通讯作者：
P. Teichner
中科院分区：
文献类型：
--
作者：
James F. Conant;P. Teichner
我们解释了费曼图的常用代数在[CT]中引入的摸索度下的行为。我们证明了用“类”来组织群时，Kontsevich积分对3空间中结点的群协进行了合理的分类。这意味着在三维空间中，grop协等值关系是高度非平凡的。我们还表明，在4维中，类不是有用的组织复杂性，因为只有Arf不变量存在。相比之下，根据“高度”测量gropes确实会产生非常有趣的四维信息[COT]。最后，我们解释了几个低次的计算，特别是我们证明了s等价与基于具有内顶点的最小树的grop协同是相同的关系。
We explain how the usual algebras of Feynman diagrams behave under the grope degree introduced in [CT]. We show that the Kontsevich integral rationally classifies grope cobordisms of knots in 3-space when the ‘‘class’’ is used to organize gropes. This implies that the grope cobordism equivalence relations are highly nontrivial in dimension 3. We also show that the class is not a useful organizing complexity in 4 dimensions since only the Arf invariant survives. In contrast, measuring gropes according to ‘‘height’’ does lead to very interesting 4-dimensional information [COT]. Finally, several low degree calculations are explained, in particular we show that S-equivalence is the same relation as grope cobordism based on the smallest tree with an internal vertex.