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We give topological obstructions to the existence of a closed exactLagrangian submanifold in the cotangent bundle of a closed manifold M which isthe total space of a fibration over the circle. For instance we show that thefundamental group of such a Lagrangian submanifold cannot be the free productof two non-trivial groups and that in any finite presentation of this group thedifference between the number of generators and the number of relations is lessthan two.

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