Infinitely many leaf-wise intersections on cotangent bundles

2008/12/31 by Peter Albers, Urs Frauenfelder · 32 citations
Mathematics · #Algebraic Geometry and Number Theory #Closed manifold #Combinatorics #Cotangent bundle #Geometric and Algebraic Topology #Geometry #Homology (biology) #Homotopy and Cohomology in Algebraic Topology #Intersection (aeronautics) #Invariant manifold #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Pure mathematics #Trigonometric functions #math.DS #math.SG #msc:37J10 #msc:53D40 #msc:58J05

paper · pdf · doi:10.1016/j.exmath.2012.01.005

published in Expositiones Mathematicae 30(2), 168-181 (Elsevier BV) · 7 pages, 1 figure; v2: completely rewritten, improved results

arxiv created 2009/11/04 · openalex publication_date 2012/01/01 · arxiv updated 2012/08/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Contact geometry of the restricted three‐body problem
• Regularization of kepler's problem and the averaging method on a manifold
• Introduction to Symplectic Field Theory