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

Abstract

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

References in corpus (2)

• Microlocal branes are constructible sheaves
• The symplectic geometry of cotangent bundles from a categorical viewpoint

Cited by in corpus (2)

• Floer homology on the universal cover, a proof of Audin's conjecture and other constraints on Lagrangian submanifolds
• Higher rank local systems in Lagrangian Floer theory