Speaker: Mark McLean（Stony Brook University）
Time: 09:30-10:30, Mar 9, 2023
Room: Zoom Meeting: 841 2143 4035, password: 462059
Consider a smooth submersion from a symplectic manifold P to the complex line with symplectic fibers. Then we prove that the cohomology of P over the integers is additively isomorphic to the cohomology of the fiber times the base. More generally, we prove such an isomorphism holds with respect to any complex oriented cohomology theory, such as complex cobordism. These results are new even in the special case of smooth projective morphisms to the complex line. To prove our result we use Morava K theories. Our proof also contains a new construction of a global Kuranishi chart for the moduli space of curves. We will mainly focus on the construction of global Kuranishi charts. This is joint work with Abouzaid and Smith.
