Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers
Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers
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迭代 p 覆盖中的链接一致性、同源共边性和 Hirzebruch 型缺陷
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发表时间：
2007
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通讯作者：
Jae Choon Cha
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作者：
Jae Choon Cha
我们从迭代 p 覆盖塔的 Hirzebruch 型相交形式缺陷中获得了 3 流形的拓扑链接一致性和同源协边的新不变量。我们的不变量可以从基本群的派生级数的任意深度提取几何信息，并且可以通过签名不变量检测不可见的扭转。说明这些特征的应用包括以下内容： (1) 有无限多个同源等价的有理 3-球体，它们通过多重签名、eta 不变量和 L2 签名无法区分，但具有不同的同源协调类型。 (2) 存在无限系列的 2 扭转（两性）结，包括八字结，具有非切片迭代 Bing 双打；作为一个特例，我们给出了八字结的Bing double不是切片猜想的第一个证明。 (3) 在链接一致性的 Cochran-Orr-Teichner 过滤的任何深度都存在无穷多个扭转元素。
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary depth of the derived series of the fundamental group, and can detect torsion which is invisible via signature invariants. Applications illustrating these features include the following: (1) There are infinitely many homology equivalent rational 3-spheres which are indistinguishable via multisignatures, eta-invariants, and L2-signatures but have distinct homology cobordism types. (2) There is an infinite family of 2-torsion (amphichiral) knots, including the figure eight knot, with non-slice iterated Bing doubles; as a special case, we give the first proof of the conjecture that the Bing double of the figure eight knot is not slice. (3) There exist infinitely many torsion elements at any depth of the Cochran-Orr-Teichner filtration of link concordance.