The Relative Fukaya Category as a Closed-Open Deformation
We give a proof of Conjecture $1.3$ of \cite{strom2024maurer}.
math.SG↗
arXiv subjects
Mohamad Rabah
Publications and source records attributed to Mohamad Rabah.
Existence of Reeb Chords from the Generation-Criteria
We give some existence results of Reeb chords using the $\textit{generation-criteria}$ of the Fukaya category. In particular, for $n\geq3$, we construct a Legendrian $\ell'\subset S^*\mathbb T^n$ such that every closed spin Legendrian $\ell\subset S^*\mathbb T^n$ either admits a self-Reeb chord or a Reeb chord joining it to $\ell'$.
math.SG↗
Fukaya Algebra over $\mathbb{Z}$
Given a closed, connected, relatively-spin Lagrangian submanifold in a closed symplectic manifold, we associate to it a curved, gapped, filtered, $A_{n, K}$-algebra over the Novikov ring with integer coefficients, which we extend to an $A_\infty$-algebra. To illustrate our framework, we give a proof of the Quantum Lefschetz Hyperplane Theorem in the K$\ddot a$hler case, and associate virtual fundamental classes to the moduli spaces used in local Gromov-Witten theory, in the symplectic case.
math.SG↗