Friday March 24th, 2023 | |
| Time: | 1:30 PM - 3:00 PM |
| Title: | Obstructions for exact submanifolds with symplectic applications |
| Speaker: | Kevin Sackel, University of Massachusetts-Amherst |
| Location: | Math 4-130 |
| Abstract: | |
| Suppose a closed oriented manifold comes with a fixed real cohomology class. This cohomology class singles out those submanifolds for which the restriction of the given cohomology class is trivial. We may ask in what integral homology classes we find such "exact submanifolds." We build an infinite sequence of obstructions which are readily computable by (finite-dimensional) linear algebra performed on the de Rham complex. As the impetus for this work arose out of (locally conformal) symplectic geometry, which we shall partially describe, our main applications are symplectic in nature. For example, the following symplectic manifolds admit no non-separating (a fortiori contact-type) hypersurfaces: Kähler manifolds, symplectically uniruled manifolds, and the Kodaira-Thurston manifold. | |