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We use quilted Floer theory to construct functor-valued invariants of tangles arising from moduli spaces of flat bundles on punctured surfaces. As an application, we show the non-triviality of certain elements in the symplectic mapping class groups of moduli spaces of flat bundles on punctured spheres.
We construct partial category-valued field theories in (2+1)-dimensions using Lagrangian Floer theory in moduli spaces of central-curvature unitary connections with fixed determinant of rank r and degree d where r,d are coprime positive integers. The
In all known explicit computations on Weinstein manifolds, the self-wrapped Floer homology of non-compact exact Lagrangian is always either infinite-dimensional or zero. We show that a global variant of this observed phenomenon holds in broad general
We study threefolds $Y$ fibred by $A_m$-surfaces over a curve $S$ of positive genus. An ideal triangulation of $S$ defines, for each rank $m$, a quiver $Q(Delta_m)$, hence a $CY_3$-category $(C,W)$ for any potential $W$ on $Q(Delta_m)$. We show that
We introduce a class of Liouville manifolds with boundary which we call Liouville sectors. We define the wrapped Fukaya category, symplectic cohomology, and the open-closed map for Liouville sectors, and we show that these invariants are covariantly
In this paper, we discuss Floer homology of Lagrangian submanifolds in an open symplectic manifold given as the complement of a smooth divisor. Firstly, a compactification of moduli spaces of holomorphic strips in a smooth divisor complement is intro