Application of knot theory to biology

我们研究了带状手术和Dehn手术，并将其结果应用于酶作用于DNA的研究，得到以下结果：（1）最多7个交叉的结和环面之间的带状手术的特征。(2)使用+- unknotting操作和-+ unknotting操作表征结。(3)简单立方晶格中板状区域纽结最小步数的研究。(4)Xer位点特异性重组在链烷上产生结的研究。(5)具有非平凡因子纽结的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评论论文中。

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.