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Shake Slice and Shake Concordant Links

机译:摇动切片和摇动一致链接

摘要

The study of knots and links up to concordance has proved significant for many problems in low dimensional topology. In the 1970s, Akbulut introduced the notion of shake concordance of knots, a generalization of the study of knot concordance. Recent work of Cochran and Ray has advanced our understanding of how shake concordance relates to concordance, although fundamental questions remain, especially for the class of shake slice knots. We extend the notion of shake concordance to links, generalizing much of what is known for knots, and offer a characterization in terms of link concordance and the infection of a link by a string link. We also discuss a number of invariants and properties of link concordance which extend to shake concordance of links, as well as note several that do not. Finally, we give several obstructions to a link being shake slice.
机译:对于低维拓扑中的许多问题,结节和链接的协调性研究已被证明具有重要意义。在1970年代,Akbulut引入了结的摇动一致性的概念,这是对结动一致性研究的概括。尽管仍然存在一些基本问题,尤其是对于摇片结的类别,但Cochran和Ray的最新工作使我们对摇调和声与调和之间的关系有了更深入的了解。我们将摇动一致性的概念扩展到链接,概括了许多已知的结,并就链接一致性和字符串链接对链接的感染进行了描述。我们还讨论了链接一致性的一些不变性和属性,这些不变性和性质扩展到摇晃链接的一致性,并注意到其中一些不变量和属性。最后,我们给被摇动的链接提供了一些障碍。

著录项

  • 作者

    Bosman Anthony Michael;

  • 作者单位
  • 年度 2017
  • 总页数
  • 原文格式 PDF
  • 正文语种 eng
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