Geometric Filtrations of Classical Link Concordance
Geometric Filtrations of Classical Link Concordance
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经典链接一致性的几何过滤
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Teichner
中科院分区：
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作者：
James F. Conant;Rob Schneiderman;P. Teichner
本文分别从类和阶两个方面描述了经典连杆协调类集上的grope滤波和Whitney tower滤波。利用惠特尼塔的树值相交理论，证明了相关的分级商是在一个（令人惊讶的）定义良好的连通和操作下有限生成的阿贝尔群。还介绍了扭曲的惠特尼塔，以及相应的二次增强的框架惠特尼塔的交叉理论，测量惠特尼盘框架障碍。加强了框架设置下的阻碍理论，用精确序列描述了扭曲滤波和框架滤波之间的关系，说明了高阶Sato-Levine和高阶Arf不变量是如何阻碍扭曲惠特尼塔的框架。结合文献{CST2，CST3，CST4}对过滤结果进行分类；参见我们的调查引用{CST0}以及引言的末尾。更新：本文已完全纳入论文“经典链接的惠特尼塔索引”引用{WTCCL}。
This paper describes grope and Whitney tower filtrations on the set of concordance classes of classical links in terms of class and order respectively. Using the tree-valued intersection theory of Whitney towers, the associated graded quotients are shown to be finitely generated abelian groups under a (surprisingly) well-defined connected sum operation. Twisted Whitney towers are also introduced, along with a corresponding quadratic enhancement of the intersection theory for framed Whitney towers that measures Whitney-disk framing obstructions. The obstruction theory in the framed setting is strengthened, and the relationships between the twisted and framed filtrations are described in terms of exact sequences which show how higher-order Sato-Levine and higher-order Arf invariants are obstructions to framing a twisted Whitney tower. The results from this paper combine with those in cite{CST2,CST3,CST4} to give a classifications of the filtrations; see our survey cite{CST0} as well as the end of the introduction. UPDATE: This paper has been completely subsumed into the paper "Whitney tower concordance of classical links" cite{WTCCL}.