EVENT DETAILS AND ABSTRACT

Title: Floer cohomology, Lagrangian surgery and analysis of pseudo-holomorphic polygons
Speaker: Professor Yong-Geun Oh
Speaker Info: Univeristy of Wisconsin, Madison
Brief Description:
Special Note:
Abstract:

``The analytic ingredient for the study of Floer cohomology and its enhancement, the Fukaya category, concerns the moduli space of pseudo-holomorphic polygons with its boundary edges lying on a chain of Lagrangian submanifolds in a given symplectic manifold. In this talk, I will explain a fine structure of the moduli space of pseudo-holomorphic polygons that appears in the definition of Fukaya category, and present its application to the study of metamorphosis of (k+1)-gons to k-gons under the Lagrangian surgery. Lagrangian surgery is one of the important constructions in symplectic geometry which also has a direct implication to the homological mirror symmetry.

I will also indicate how this analysis gives rise to a long exact sequence of Floer cohomology that is associated to the Dehn twist on closed Calabi-Yau manifolds. Seidel originally considered such construction for the exact Lagrangian cases on open symplectic manifolds and left out as an open problem for the closed Calabi-Yau case : This is the case that is most relevant in relation to the homological mirror symmetry.''