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A note on the weak splitting number
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-01-21 , DOI: 10.1090/proc/15177 Alberto Cavallo , Carlo Collari , Anthony Conway
Proceedings of the American Mathematical Society ( IF 1 ) Pub Date : 2021-01-21 , DOI: 10.1090/proc/15177 Alberto Cavallo , Carlo Collari , Anthony Conway
Abstract:The weak splitting number 
of a link 
is the minimal number of crossing changes needed to turn 
into a split union of knots. We describe conditions under which certain 
-valued link invariants give lower bounds on 
. This result is used both to obtain new bounds on 
in terms of the multivariable signature and to recover known lower bounds in terms of the 
and 
-invariants. We also establish new obstructions using link Floer homology and apply all these methods to compute 
for all but two of the 
prime links with nine or fewer crossings.
中文翻译：
关于弱分割数的注释
摘要：链接的弱分裂数是变成结的分裂并集所需的最小交叉变化数。我们描述了某些条件下的条件，其中某些值链接不变式给出的下界。这一结果既用来获得新的边界在多变量签名的范围，并在条件恢复已知的下限和-invariants。我们还使用链接Floer同源性建立新的障碍物，并将所有这些方法应用于除两个主要链接之外（九个或更少）的所有主要链接的计算。
更新日期：2021-02-08
of a link is the minimal number of crossing changes needed to turn into a split union of knots. We describe conditions under which certain -valued link invariants give lower bounds on . This result is used both to obtain new bounds on in terms of the multivariable signature and to recover known lower bounds in terms of the and -invariants. We also establish new obstructions using link Floer homology and apply all these methods to compute for all but two of the prime links with nine or fewer crossings. 中文翻译：
关于弱分割数的注释
摘要：链接的弱分裂数是变成结的分裂并集所需的最小交叉变化数。我们描述了某些条件下的条件，其中某些值链接不变式给出的下界。这一结果既用来获得新的边界在多变量签名的范围，并在条件恢复已知的下限和-invariants。我们还使用链接Floer同源性建立新的障碍物，并将所有这些方法应用于除两个主要链接之外（九个或更少）的所有主要链接的计算。
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