PSU Mathematics Department - Meeting Details

For more information about this meeting, contact Augustin Banyaga.

Abstract:
Title:	Length minimizing paths in the group of hamitonian diffeomorphismsdiffeomorphisms with applications to Ham(M,\omega).
Seminar:	Symplectic Topology Seminar
Speaker:	Peter Spaeth, PSU
On any closed symplectic manifold we construct a path-connected neighborhood of the identity within the Hamiltonian diffeomorphism group with the property that each Hamiltonian diffeomorphism in this neighborhood admits a Hofer and spectral length minimizing path to the identity. This neighborhood is open in the $C^1-$topology. The construction depends on a continuation argument in the spirit of the work of Y. Chekanov and a chain level result in the Floer theory of Lagrangian intersections. This generalizes results of Lalonde and McDuff, McDuff and Y.-G. Oh. While the proof is somewhat technical, effort will be made to present the argument from scratch. Of independent interest, Y.-G. Oh's spectral metric, which is a Floer theoretical refinement of the Hofer metric and Oh's homological area of will be presented in detail. Several open questions will also be addressed.