Moduli spaces for Floer theory of singular Lagrangian submanifolds

2014 Fiscal Year Final Research Report

• Project/Area Number: 23740123
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Global analysis
• Research Institution: Tokyo Metropolitan University
• Principal Investigator: AKAHO Manabu 首都大学東京, 理工学研究科, 准教授 (30332935)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: シンプレクティック幾何 / ラグランジュ部分多様体 / フレアー理論

Outline of Final Research Achievements

The purpose of this research is to construct Floer theory for singular Lagrangian submanifolds. To begin with, the researcher considered Morse functions on manifolds with boundary whose gradient vector fields are tangent to the boundary. Then he defined Morse complex for such Morse functions and succeeded in getting intersection products, which satisfies the Leibniz rules. But there are still many difficulties to construct Floer theory for singular Lagrangian submanifolds, and we would expect more future works. On the other hand, the researcher proved an inequality of symplectic displacement energy for exact Lagrangian immersions as an application of Floer homology for Lagrangian immersions, and moreover, we obtain some new conjectures.

Free Research Field

ラグランジュ部分多様体のフレアー理論