Geometric construction of modular functors based on Chern-Simons type theories

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740051
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Geometry
• Research Institution: Shinshu University
• Principal Investigator: GOMI Kiyonori 信州大学, 学術研究院理学系, 准教授 (00543109)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: Ｋ理論 / ねじれＫ理論 / 「実」ベクトル束 / 「四元数」ベクトル束 / ＦＫＭＭ不変量 / カイラルベクトル束 / 位相的絶縁体

Outline of Final Research Achievements

First, I proved a basic property of the Chern character defined for a finite dimensional model of twisted K-theory, and gave an algebro-topological interpretation of so-called Mickelsson's invariant and its generalization. I also proved topological T-dualities for "Real" circle bundles, etc. Then, we classified "Real" and "Quaternionic" vector bundles in low dimension, and studied in detail the FKMM invariant that plays a basic role in the classification of "Quaternionic" bundles. Moreover, we introduced chiral vector bundles and carried out the same classification as above. We also computed twisted K-thoery to discover a new topological insulating phenomena classified by Z/2.

Free Research Field

位相幾何学