Discrete quantization of low-dimensional geometry with quantum invariants

2016 Fiscal Year Final Research Report

• Project/Area Number: 25287014
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Partial Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Waseda University
• Principal Investigator: Murakami Jun 早稲田大学, 理工学術院, 教授 (90157751)
• Co-Investigator(Kenkyū-buntansha): 水澤 篤彦 早稲田大学, 理工学術院, 助教 (50707726)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Keywords: 低次元トポロジー / 量子不変量 / 双曲幾何学 / ３次元多様体 / 結び目

Outline of Final Research Achievements

The aim of this research is to construct discretized quantum geometry for 2 and 3 dimensional case. To do this, various quantum invariants and their relations are studied. For example, we study the colored Jones invariant, the colored Alexander invariant, the Hennings invariant and the logarithmic invariant. Quantum invariants for knotted graphs and its relation to the geometric structure is also studied. Especially, we get the relation between quantum invariants and hyperbolic volume determined by the geometric structure for various quantum invariants.

Free Research Field

トポロジー