Unexpected connections between Burnside groups and knot theory.
Unexpected connections between Burnside groups and knot theory.
复制标题
伯恩赛德群和纽结理论之间的意外联系。
DOI：
10.1073/pnas.0406098101
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发表时间：
2003
影响因子：
11.1
通讯作者：
J. Przytycki
中科院分区：
文献类型：
--
作者：
M. Dabkowski;J. Przytycki
在经典的纽结理论和量子不变量理论中，大量的努力都是针对寻找解开链接的动作。在这篇文章中，我们解决了几个经典的问题，有关unknoting移动。我们的方法使用了一个概念，伯恩赛德集团的联系，建立了一个意想不到的纽结理论和群论之间的关系。我们的方法有可能被用于计算生物学中的DNA分析通过缠结嵌入理论，如D。W. Sumners，D. W.，编辑。（1992）几何和拓扑学的新科学应用（Am Math. Soc.，华盛顿，DC）和Ernst，C. & Sumners，D. W.（1999）Math. Proc.剑桥Philos.Soc.126，23-36]。
In classical knot theory and the theory of quantum invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this article, several classical problems concerning unknotting moves. Our approach uses a concept, Burnside groups of links, that establishes an unexpected relationship between knot theory and group theory. Our method has the potential to be used in computational biology in the analysis of DNA via tangle embedding theory, as developed by D. W. Sumners [Sumners, D. W., ed. (1992) New Scientific Applications of Geometry and Topology (Am Math. Soc., Washington, DC) and Ernst, C. & Sumners, D. W. (1999) Math. Proc. Cambridge Philos. Soc. 126, 23-36].