
## 3. SFT

1. #### Problem 3.1.

Completeness of the SFT Hamiltonian system i.e. do the Hamiltonians $h_{\alpha,i}$ form a maximal commuting set in $H_*(\mathcal{P})?$

In particular, in the case of symplectic mapping tori, use the relation to Floer theory of the underlying symplectomorphism to find appropriate generalizations of Frobenius manifolds and bihamiltonian structures. Does there exist a flatness equation on SFT homology? Study these questions for the example of local SFT.
• #### Problem 3.2.

Can SFT be used as an invariant to distinguish lens spaces?
• #### Problem 3.3.

Computation of the commuting Hamiltonians for subcritical Stein-fillable manifolds using Legendrian SFT.

Particular example: $M=\left\{\left\{f(x_1,..,x_n)=\epsilon\neq 0\right\}\cap S^{2n+1}\right\}$ where $f(x_1,..,x_n)$ is a weighted homogenous polynomial.

Cite this as: AimPL: Integrable systems in Gromov-Witten and symplectic field theory, available at http://aimpl.org/gwsymplectic.