论文标题
Clasper Concordance，Whitney Towers和重复Milnor不变式
Clasper Concordance, Whitney towers and repeating Milnor invariants
论文作者
论文摘要
我们表明，对于\ mathbb {n} $中的每个$ k \，link $ l \ subset s^3 $在4球中限制了$ k $ whitney塔，并且仅当它是\ emph {$ emph {$ c_k $ -concordant}时。这意味着$ l $是通过有限的一致和$ k $ clasper手术从UNINB中获得的。在我们的建筑中，与惠特尼塔相关的树木与与扣子相关的树木一致。 作为我们先前针对惠特尼塔（Whitney Towers）在4球中的阻塞理论的推论，因此，链接的$ C_K $ - 符号过滤是根据Milnor不变性，高阶Sato-Levine和ARF不变的分类。 使用$ k $重复的扭曲惠特尼塔的新概念，我们还根据$ k $重新培训Milnor Invariants和$ k $ -k $ - 重新启动的Arf Invariants Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf Arf。
We show that for each $k\in\mathbb{N}$, a link $L\subset S^3$ bounds a degree $k$ Whitney tower in the 4-ball if and only if it is \emph{$C_k$-concordant} to the unlink. This means that $L$ is obtained from the unlink by a finite sequence of concordances and degree $k$ clasper surgeries. In our construction the trees associated to the Whitney towers coincide with the trees associated to the claspers. As a corollary to our previous obstruction theory for Whitney towers in the 4-ball, it follows that the $C_k$-concordance filtration of links is classified in terms of Milnor invariants, higher-order Sato-Levine and Arf invariants. Using a new notion of $k$-repeating twisted Whitney towers, we also classify a natural generalization of the notion of link homotopy, called twisted \emph{self $C_k$-concordance}, in terms of $k$-repeating Milnor invariants and $k$-repeating Arf invariants.
