Application of knot theory to biology

我们对带状外科和Dehn外科进行了研究，并将研究结果应用于酶作用于DNA的研究中。我们得到了以下结果：(1)最多有7个交叉和环状连接的结之间的带状外科的特征。(2)具有+-解结操作和-+解结操作的纽结的特征。(3)简立方晶格中平板区域最小节点数的研究。(4)顺丁烯基环戊二烯的Xer定点重组研究。(5)具有非平凡因子的纽结的A-多项式的研究。这些成果已发表在论文、国际会议特邀演讲和综述论文中。

We studied band surgery and Dehn surgery and applied the results to studies of enzyme acting on DNA.The results we obtained are the followings: (1) Characterization of band surgeries between knots with at most 7 crossing and torus links. (2) Characterization of knots with a +- unknotting operation and a -+ unknotting operation. (3) Study of minimum step number of knots in a slab region in the simple cubic lattice. (4) Study of Xer site-specific recombination on a catenane yielding a knot. (5) Study of A-polynomials of knots with non-trivial factors. These results have been published in papers, invited talks in international conferences, and review papers.