Northern California Symplectic Geometry Seminar: Divisor complements in Calabi-Yau symplectic manifolds

Seminar | May 6 | 2:30-3:30 p.m. | 384H STANFORD

 Umut Varolgunes, Stanford

 Department of Mathematics

Let $(M,\omega )$ be a closed symplectic manifold. Consider a closed symplectic submanifold $D$ whose homology class is a positive multiple of the Poincare dual of $[\omega ]$. The complement of $D$ can be given the structure of a Liouville manifold, with skeleton $S$. We prove that $S$ cannot be displaced from itself inside $M$ by a Hamiltonian isotopy if we assume that $c_1(M)=0$. Under the same assumption, we also prove that Floer theoretically essential Lagrangians in $M$ have to intersect $S$. These results are related to an understanding of the notions heavy and superheavy in terms of relative symplectic cohomology. Ongoing joint work with Dmitry Tonkonog.