Feral pseudoholomorphic curves and minimal sets

GAUGE-TOPOLOGY-SYMPLECTIC

Speaker:

Joel Fish - UMass Boston

Abstract:

I will discuss some recent joint work with Helmut Hofer, in which we define and establish properties of a new class of pseudoholomorhic curves (feral J-curves) to study certain divergence free flows in dimension three. In particular, we show that if H is a smooth, proper, Hamiltonian in R^4, then no regular non-empty energy level of H is minimal. That is, the flow of the associated Hamiltonian vector field has a trajectory which is not dense.