
On the Topological Invariance of Helicity
Oliver Edtmair, of ETH Zurich, presents a proof that helicity, the classical invariant of divergence free vector fields on a three manifold, extends to topological volume preserving flows and remains invariant under volume preserving homeomorphisms. The talk, given for the joint IAS Princeton Montreal Paris Tel Aviv Symplectic Geometry Zoominar, traces the question back to Arnold, who interpreted helicity as an asymptotic Hopf invariant via ergodic theory and asked whether it survives the passage from diffeomorphisms to mere homeomorphisms. Edtmair answers both of Arnold's questions affirmatively for non-singular flows, drawing on recent work in C0 symplectic geometry, particularly the algebraic structure of the group of area preserving homeomorphisms, which he surveys along the way. The work is joint with Sobhan Seyfaddini. The talk assumes graduate level familiarity with symplectic and fluid topology and runs through the main lemmas behind the proof.