Research on Floer theory of singular Lagrangian submanifolds

在这项资助中，研究工作者研究了奇异拉格朗日子流形的花理论。他特别考虑了以下两种情况；第一类是浸入式拉格朗日子流形，第二类是凹端辛流形中具有勒让端的拉格朗日子流形。对于第一种情况，他得到了具有横向双奇点的浸入式拉格朗日子流形的a -∞代数，这是与D. Joyce的联合工作。其次，在无泡假设下，构造了两个具有勒让端的拉格朗日子流形的花同调。此外，他还研究了具有边界的流形的Morse同伦，得到了杯积的定义，给出了具有Legendrian端点的拉格朗日子流形的a -∞代数方向。

In this grant, the research worker studied Floer theory for singular Lagrangian submanifolds. In particular, he considered the following two cases ; first, immersed Lagrangian submanifolds, and secondly, Lagrangian submanifolds with Legendrian end in a symplectic manifold with concave end. For the first case, he obtained A-infinity algebras of immersed Lagrangian submanifolds with transverse double singularities, which is a joint work with D. Joyce. Secondly, he constructed Floer homology for two Lagrangian submanifolds with Legendrian end, under no bubble assumption. Moreover, he studied Morse homotopy for manifolds with boundary and obtain the definition of cup products, which tells us the direction towards A-infinity algebras of Lagrangian submanifolds with Legendrian end.