低次元トポロジーの総合的研究

2001年学术年：我们在数学科学研究所和京都大学研究所组织了一个长期研究项目“21世纪的低维度拓扑学”，我们邀请了日本内外的低维度拓扑学家。我们有大约50位来自海外的访问者，我们可以交换信息，并在不同地区讨论，包括许多讲座。当然，我们可以在低尺寸拓扑的许多区域中找到新的方面，例如三尺寸块的组合研究、四尺寸块的已知表面以及knot和三尺寸块的量子变量。2002年学术年：我们公布了我们在2001年学术年获得的结果。我们也用研究人员改变了想法，并可以实现我们的新目标。4月，首席调查员和村上春树邀请参加了在魁北克大学蒙特利尔、加拿大和Gave谈话中指导的一个讲习班。体积概念是由Murakami Jun和首席调查员生成R提出的。Kashaev的概念。它将把彩色琼斯的轮廓与结互补的几何结构和许多研究人员的吸引力联系起来。7月访问韩国科学和技术高级研究所，并提供了一系列关于三尺寸清单的讲座。Taniyama在国际会议“几何拓扑”上发表了关于图表链接的邀请讲座，由中国西安。Ohtsuki出版了一本名为《量子变量》的书，《量子变量》的研究、3块和他们的一套》，其中描述了量子变量，包括他自己的结果。

The academic year 2001: We organized the yearlong Research Project 'Low-Dimensional Topology in the 21st Century' at the Research Institute for Mathematical Sciences, Kyoto UniversityIn this project we invited low-dimensional topologists from inside and outside Japan. We had about 50 visitors from overseas and we could exchange information and could discuss on various areas with many lectures. Consequently we could obtain new aspects on many areas in low-dimensional topology such as combinatorial study of three-dimensional manifolds, knotted surfaces in four-dimensional manifolds, and quantum invariants of knots and three-manifolds.The academic year 2002 : We publicized our results obtained in the academic year 2001. We also exchanged ideas with researchers and thus could make our new goals.In April the head investigator and Jun Murakami were invited to a workshop on the volume conjecture held at the University of Quebec at Montreal, Canada and gave talks. The volume conjecture was proposed by Jun Murakami and the head investigator generalizing R. Kashaev's conjecture. It would relate the colored Jones polynomials of knots to the geometric structures of the knot complements, and attracts many researchers all over the world. Kobayashi visited Korea Advanced Institute for Science and Technology in July and gave a series of lectures on three-dimensional manifolds. Taniyama gave an invited lecture on links in graphs at the international conference 'Geometric Topology' held at Xian, China. Ohtsuki published a book 'Quantum invariants ・・A study of knots, 3-manifolds, and their sets', which describes quantum invariants including his own results.