基于扭曲Whitney塔的Cochran $β^i$不变量
Cochran's $β^i$ invariants via twisted Whitney towers
摘要：
我们表明，蒂姆Cochran的不变量$β^i(L)$的一个$2$组件链接$L$在$3$ -球可以计算为相交不变量的某些2-复合物在$4$ -球与边界$L$。这些2-复合物是特殊类型的扭曲惠特尼塔，我们称之为{ \em Cochran塔}，并表现出一个新的现象：一个Cochran塔的顺序$2k$允许计算的$β^i$不变量的所有$i\leq k$，即同时提取不变量的惠特尼塔在多个订单。这与阶$n$ Milnor不变量（需要阶$n$ Whitney塔）相反，并且与Cochran的结果一致，即$β^i(L)$是某些Milnor不变量的整数提升。
英文摘要：
We show that Tim Cochran's invariants $β^i(L)$ of a $2$-component link $L$ in the $3$--sphere can be computed as intersection invariants of certain 2-complexes in the $4$--ball with boundary $L$. These 2-complexes are special types of twisted Whitney towers, which we call {\em Cochran towers}, and which exhibit a new phenomenon: A Cochran tower of order $2k$ allows the computation of the $β^i$ invariants for all $i\leq k$, i.e. simultaneous extraction of invariants from a Whitney tower at multiple orders. This is in contrast with the order $n$ Milnor invariants (requiring order $n$ Whitney towers) and consistent with Cochran's result that the $β^i(L)$ are integer lifts of certain Milnor invariants.
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