Geometry of moduli spaces and application to topological field theory

2015 Fiscal Year Final Research Report

• 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
• 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

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.

Free Research Field

複素多様体論