Constraints on Exact Lagrangians in Cotangent Bundles of Manifolds Fibered over the Circle

We give topological obstructions to the existence of a closed exact Lagrangian submanifold L →֒ T M , where M is the total space of a fibration over the circle. For instance, we show that π1(L) cannot be the free product of two non-trivial groups and that the difference between the number of generators and the number of relations in a finite presentation of… CONTINUE READING