Quantum cohomology as a deformation of symplectic cohomology

Abstract: Consider a positively monotone closed symplectic manifold $M$ and a symplectic simple crossings divisor $D$ in it. Assume that the Poincare dual of the anti-canonical class is a positive rational linear combination of the classes $[D_i]$, where $D_i$ are the components of $D$ with their symplectic orientation. A choice of such coefficients, called the weights, (roughly speaking) equips $M-D$ with a Liouville structure. I will start by discussing results relating the symplectic cohomology of $M-D$ with quantum cohomology of $M$. These results are particularly sharp when the weights are all at most 1 (hypothesis A). Then, I will discuss certain rigidity results (inside $M$) for skeleton type subsets of $M-D$, which will also demonstrate the geometric meaning of hypothesis A in examples. The talk will be mainly based on joint work with Strom Borman and Nick Sheridan.

algebraic geometrydifferential geometrygeometric topologysymplectic geometry

Audience: researchers in the topic

Free Mathematics Seminar

Series comments: This is the free mathematics seminar. Free as in freedom. We use only free and open source software to run the seminar.

The link to each week's talk is sent to the members of the e-mail list. The registration link to this mailing list is available on the homepage of the seminar.