低次元トポロジーの総合的研究

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 about50visitors 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 year2001。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.

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.