Loop products and closed geodesics
Copyright policy )Loop products and closed geodesics
We show the Chas-Sullivan product (on the homology of the free loop space of a Riemannian manifold) is related to the Morse index of its closed geodesics. We construct related products in the cohomology of the free loop space and of the based loop space, and show they are nontrivial.
63 pages
- College of New Jersey United States
- Institute for Advanced Study United States
Mathematics - Differential Geometry, 58E10, 53C22, FOS: Mathematics, 53C, Algebraic Topology (math.AT), Products and intersections in homology and cohomology, Mathematics - Algebraic Topology, 53C22, 37B30, closed geodesics, 55N, 57R, Sullivan's coproduct, String topology, loop products, 55N45; 53C22, 37B30, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Geodesics in global differential geometry, 58E05, Morse index, Differential Geometry (math.DG), 55N45, cohomology, ring structure, geodesic, Variational problems in applications to the theory of geodesics (problems in one independent variable)
Mathematics - Differential Geometry, 58E10, 53C22, FOS: Mathematics, 53C, Algebraic Topology (math.AT), Products and intersections in homology and cohomology, Mathematics - Algebraic Topology, 53C22, 37B30, closed geodesics, 55N, 57R, Sullivan's coproduct, String topology, loop products, 55N45; 53C22, 37B30, Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces, Geodesics in global differential geometry, 58E05, Morse index, Differential Geometry (math.DG), 55N45, cohomology, ring structure, geodesic, Variational problems in applications to the theory of geodesics (problems in one independent variable)
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