Geometry of moduli spaces and application to topological field theory
Project/Area Number |
24540045
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Tokyo Metropolitan University |
Principal Investigator |
Ueno Kenji 首都大学東京, 理工学研究科, 客員教授 (40011655)
|
Project Period (FY) |
2012-04-01 – 2016-03-31
|
Project Status |
Completed (Fiscal Year 2015)
|
Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
|
Keywords | 共形場理論 / 位相的場の理論 / モジュライ空間 / 不変量 / 射影的平坦続 / 閉リーマン面 / 代数曲線 / 重複ファイバー / 共形場ブロック / 接続 / ベクトル束 / モノドロミー表現 / アフィンリー代数 / モジュラー函手 / 射影的平坦接続 / 曲線の退化 / 国際研究者交流,デンマーク / TUY接続 / Hitchin接続 / ヘッケ代数 |
Outline of Final Research Achievements |
With J. E. Andersen from conformal field theory I constructed modular functors, which give invariants of 3-manifolds. When the gauge group is sl(n,C) we proved that the invariants of 3-manifolds are the same to the those constructed by Reshetikhin and Turaev. We also show that the projectively flat connection of the conformal field theory coincides with the one defined by Hitchin when the gauge group is sl(2,C) and level 1. This was the only exceptional case that the isomorphism was not known. Also in characteristic p >0 multiple fibers pF whose underling configurations F are degenerations of curves of genus 2 were constructed.
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Report
(5 results)
Research Products
(7 results)