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.
Cite this article
Mihai Damian, Constraints on exact Lagrangians in cotangent bundles of manifolds fibered over the circle. Comment. Math. Helv. 84 (2009), no. 4, pp. 705–746DOI 10.4171/CMH/178