Infinitely many leaf-wise intersections on cotangent bundles

TL;DR

This paper proves that for certain hypersurfaces in cotangent bundles of manifolds with infinite-dimensional free loop space homology, there are infinitely many leaf-wise intersection points.

Contribution

It establishes a generic existence result for infinitely many leaf-wise intersections on cotangent bundles under specific topological conditions.

Findings

Infinite leaf-wise intersections exist under the given conditions.

The result applies to fiber-wise star-shaped hypersurfaces.

It links the topology of the free loop space to symplectic geometry.

Abstract

If the homology of the free loop space of a closed manifold B is infinite dimensional then generically there exist infinitely many leaf-wise intersection points for fiber-wise star-shaped hypersurfaces in T*B.