EVENT DETAILS AND ABSTRACT

Title: Novikov-symplectic cohomology and exact Lagrangian embeddings
Speaker: Alexander Ritter
Speaker Info: MIT
Brief Description:
Special Note:
Abstract:

We are interested in finding topological obstructions to the existence of exact Lagrangian submanifolds L inside a cotangent bundle T^*N. We assume N is simply connected, but we make no assumptions on the Maslov class of L. We prove that H^2(N) injects into H^2(L) and that the image of \pi_2(L) in \pi_2(N) has finite index. A more complicated statement holds in the non-simply connected case. Our approach builds on Viterbo's work: by using symplectic cohomology we construct a transfer map on the Novikov homologies of the free loop spaces of N and L. The above application is then a consequence of the vanishing of the Novikov homology of the free loopspace with respect to non-zero 1-forms.