Prof. F. Schlenk (Neuchatel)

Action selectors without Floer homology

Abstract: An action selector associates to every Hamiltonian function the action of one of its periodic orbits, in a continuous way. The mere existence of an action selector has many consequences in symplectic dynamics and geometry (like Gromov’s non-squeezing theorem and the existence of closed orbits on energy surfaces of contact type). The first selectors were constructed for the standard symplectic vector space 2n by Viterbo and Hofer-Zehnder, and then for (essentially) all symplectic manifolds by means of Floer homology (Schwarz, Oh, Usher). I will describe a more elementary construction of an action selector for manifolds (M,ω) with [ω]|π2(M) = 0, that uses only Gromov compactness.
This is joint work with Alberto Abbondandolo et Carsten Haug.