Algebraic and category-theoretic study of low-dimensional topology

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540077
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Geometry
• Research Institution: Kyoto University
• Principal Investigator: Habiro Kazuo 京都大学, 数理解析研究所, 准教授 (80346064)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: 3次元多様体 / Kirby計算 / 量子群 / 圏化 / トレース / 量子不変量

Outline of Final Research Achievements

I studied several topics on 3-dimensional topology and related algebra.
Jointly with T. Widmer, I studied Kirby calculus for null-homotopic framed links and null-homologous framed links in 3-manifolds. Jointly with A. Beliakova, Z. Guliyev, A. D. Lauda, B. Webster and M. Zivkovic, I studied categorified quantum groups, in particular the ribbon element, the traces and the pivotal structure. Jointly with T. Q. T. Le, for each finite dimensional complex simple Lie algebra g, I constructed an invariant of integral homology 3-spheres which unify the quantum g invariants at various roots of unity.

Free Research Field

低次元トポロジー