Deepening and new developments of arithmetic topology

2022 Fiscal Year Final Research Report

• Project/Area Number: 17H02837
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Algebra
• Research Institution: Kyushu University
• Principal Investigator: Morishita Masanori 九州大学, 数理学研究院, 教授 (40242515)
• Project Period (FY): 2017-04-01 – 2021-03-31
• Keywords: 結び目 / 素数 / 代数体 / 3次元多様体 / 数論的位相幾何学 / 数論的位相的場の理論

Outline of Final Research Achievements

My research achievements is concerned with deepening and new developments of arithmetic topology.The outline is as follows.(1) I solved the problem posed by Deninger jointly with J. Kim, T. Noda and Y. Terashima.Namely, we showed a dynamical analog of Hilbert reciprocity law for 3-dimensional foliated dynamical system. Moreover we gave a classification of 3-dimensiona foliated dynamical systems. We published the paper on this research and I gave invited talks at conferences in Germany and US etc. (2) I constructed an arithmetic analog of (2+1)-dimensional Dijkgraaf-Witten topological quantum field theory for number rings jointly with H. Hirano and J. Kim.We published the paper on this research and I gave invited online talks at various conference and seminars. I also held the workshop at Edinburgh ``Gauge fields in Arithmetic, Topology and Physics".

Free Research Field

数論的位相幾何学

Academic Significance and Societal Importance of the Research Achievements

研究成果の学術的意義は、数論的位相幾何学という数学における新分野の創始とその深化および新展開である。社会的意義として、研究成果を査読付き国際誌に発表したこと、国内外で行われた国際研究集会で招待講演を行ったこと、さらに、本研究を契機として、2023年3月にスコットランドで「Gauge fields in Arithmetic, Topology and Physics」と題するコンファレンスを主催したこと、毎年国際研究集会「Low dimensional topology and number theory」を主催していることがあげられる。