2‐torsion in the n‐solvable filtration of the knot concordance group
2‐torsion in the n‐solvable filtration of the knot concordance group
复制标题
结索引组的 n 可解过滤中的 2-扭转
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
Constance Leidy
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作者：
Tim D. Cochran;Shelly L. Harvey;Constance Leidy
Cochran-Orr-Teichner在[‘Knot Concorance，Whitney Tower and L2-Sigures’中介绍，Ann。数学的一部分。(2)顺式C组…的自然过滤⊂Fn+1⊂Fn.5⊂Fn⊂…⊂F1⊂F0.5⊂F0⊂C，称为(N)-可解滤子。我们证明了每个相关的分次交换群{Gn=Fn/Fn.5|n∈N}，n⩾2，n⩾2，包含无穷多个线性无关的2阶元集(这是以前已知的n=0，1)。每个代表纽结都是负双标的，具有消失的S不变量、τ不变量、δ不变量和Casson-Gordon不变量。此外，每个都是有理同调4球的切片。事实上，我们证明了在Gn中有许多不同的这样的类，通过它们的Alexander多项式来区分，更一般地，通过它们的高阶Alexander模的挠度来区分。
Cochran–Orr–Teichner introduced in [‘Knot concordance, Whitney towers and L2‐signatures’, Ann. of Math. (2) 157 (2003) 433–519] a natural filtration of the smooth knot concordance group C …⊂Fn+1⊂Fn.5⊂Fn⊂…⊂F1⊂F0.5⊂F0⊂C, called the (n)‐solvable filtration. We show that each associated graded abelian group { Gn=Fn/Fn.5|n∈N },n⩾2 , n ⩾ 2, contains infinite linearly independent sets of elements of order 2 (this was known previously for n = 0, 1). Each of the representative knots is negative amphichiral, with vanishing s‐invariant, τ‐invariant, δ‐invariants and Casson–Gordon invariants. Moreover, each is slice in a rational homology 4‐ball. In fact we show that there are many distinct such classes in Gn , distinguished by their Alexander polynomials and, more generally, by the torsion in their higher‐order Alexander modules.