Topological Character of Smooth Invariants and Topologically Conjugate Smooth Dynamical SystemsNew Trends in Symplectic and Contact Geometry (GESTA) (2011)
Suppose one is given an invariant of smooth vector fields that takes the same value on X and \phi_* X for any C^1-diffeomorphism \phi. Is this invariant also invariant under topological conjugation, and is it possible to extend the invariant to isotopies of homeomorphisms (at least in the presence of some additional geometric structure that is preserved)? V. I. Arnold originally posed this question for the helicity of a divergence-free vector field on a (closed) three-manifold. A natural question in this context is whether it is possible for two smooth vector fields to be topologically conjugate but not C^1-smoothly so. For Hamiltonian and (strictly) contact vector fields, we give an affirmative answer to both questions (for many such invariants). The proofs are based on C^0-symplectic and contact topology, and this talk will survey these new tools.
Publication DateJune 29, 2011
LocationCastro Urdiales, Spain
Citation InformationStefan Müller. "Topological Character of Smooth Invariants and Topologically Conjugate Smooth Dynamical Systems" New Trends in Symplectic and Contact Geometry (GESTA) (2011)
Available at: http://works.bepress.com/stefan-muller/11/