Stabilizations, Satellites, and Exotic SurfacesAbstractA long standing question in the study of exotic behavior in dimension four is whether exotic behavior is “stable". For example, in thinking about the four-dimensional h-cobordism theorem, Wall proved that simply connected, exotic four-manifolds always become smoothly equivalent after applying a suitable stabilization operation enough times...
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...