Constraints on exact Lagrangians in cotangent bundles of manifolds fibered over the circle

Abstract

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 π1(L) is less than two.