We prove the quilted Floer cochain complexes form A infinity n-modules over the Fukaya category of Lagrangian correspondences. Then we prove that when we restrict the input to mapping cones of product Lagrangians and graphs, the resulting bar-type complex can be identified with bar complex from ordinary Floer theory. As an application we use a family version of quilt unfolding argument to prove two long exact sequences conjectured by Seidel that relates the Lagrangian Floer cohomology of a collection of (possibly intersecting) Lagrangian spheres and the fixed point Floer cohomology of composition of Dehn twists along them.

Organizers

Kenji Fukaya (YMSC)

Honghao Gao (YMSC)

Hang Yuan (BIMSA)

Speaker

Shuo Zhang 张硕

Shuo Zhang is a postdoctoral researcher at the Academy of Mathematics and Systems Science (AMSS), Chinese Academy of Sciences (CAS).

Time

Mon., 3:30-4:30 pm, May 12, 2025

Venue

B627, Shuangqing Complex Building A