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Primary decomposition of knot concordance and von Neumann rho-invariants
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-20 , DOI: 10.1090/proc/15282 Min Hoon Kim , Se-Goo Kim , Taehee Kim
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-20 , DOI: 10.1090/proc/15282 Min Hoon Kim , Se-Goo Kim , Taehee Kim
Abstract:We address the primary decomposition of the knot concordance group in terms of the solvable filtration and higher order von Neumann 
-invariants by Cochran, Orr, and Teichner. We show that for a non-negative integer 
, if the connected sum of two 
-solvable knots with coprime Alexander polynomials is slice, then each of the knots has vanishing von Neumann 
-invariants of order 
. This gives positive evidence for the conjecture that nonslice knots with coprime Alexander polynomials are not concordant. As an application, we show that if 
is one of Cochran-Orr-Teichner's knots which are the first examples of nonslice knots with vanishing Casson-Gordon invariants, then 
is not concordant to any knot with Alexander polynomial coprime to that of 
.
中文翻译：
结一致性和冯·诺依曼变容常数的初次分解
摘要：我们通过Cochran，Orr和Teichner的可解过滤和高阶冯·诺伊曼不变量解决了结一致基团的初次分解。我们证明，对于一个非负整数，如果两个可解结与互质素亚历山大多项式的连接和为切片，则每个结的阶数为von Neumann-不变式。这为猜想提供了积极的证据，即非互结与共质数亚历山大多项式不一致。作为一个应用，我们表明，如果是Cochran-Orr-Teichner的结中的一个，这是具有Casson-Gordon不变量消失的非切片结的第一个示例，那么与亚历山大多项式互质数的任何结都不相符。。
更新日期：2020-11-12
-invariants by Cochran, Orr, and Teichner. We show that for a non-negative integer , if the connected sum of two -solvable knots with coprime Alexander polynomials is slice, then each of the knots has vanishing von Neumann -invariants of order . This gives positive evidence for the conjecture that nonslice knots with coprime Alexander polynomials are not concordant. As an application, we show that if is one of Cochran-Orr-Teichner's knots which are the first examples of nonslice knots with vanishing Casson-Gordon invariants, then is not concordant to any knot with Alexander polynomial coprime to that of . 中文翻译：
结一致性和冯·诺依曼变容常数的初次分解
摘要：我们
通过Cochran，Orr和Teichner的可解过滤和高阶冯·诺伊曼不变量解决了结一致基团的初次分解。我们证明，对于一个非负整数，如果两个可解结与互质素亚历山大多项式的连接和为切片，则每个结的阶数为von Neumann-不变式。这为猜想提供了积极的证据，即非互结与共质数亚历山大多项式不一致。作为一个应用，我们表明，如果是Cochran-Orr-Teichner的结中的一个，这是具有Casson-Gordon不变量消失的非切片结的第一个示例，那么与亚历山大多项式互质数的任何结都不相符。。 
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