相关论文: Fukaya categories of orbifold surfaces in represen…
We give a complete description of partially wrapped Fukaya categories of graded orbifold surfaces with stops. We show that a construction via global sections of a natural cosheaf of A$_\infty$ categories on a Lagrangian core of the surface…
In this paper we use recollements to investigate partially wrapped Fukaya categories of surfaces with marked points. In particular, we show that cutting surfaces gives rise to recollements of the corresponding partially wrapped Fukaya…
We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the…
We give a complete description of the A$_\infty$ deformation theory of partially wrapped Fukaya categories of graded surfaces. We show that any abstract A$_\infty$ deformation is "geometric", namely it is equivalent to the partially wrapped…
We compute the derived Picard groups of partially wrapped Fukaya categories of surfaces in the sense of Haiden-Katzarkov-Kontsevich and the related graded gentle algebras. This includes the wrapped cases as introduced by Bocklandt. An…
We embed triangulated categories defined by quivers with potential arising from ideal triangulations of marked bordered surfaces into Fukaya categories of quasi-projective 3-folds associated to meromorphic quadratic differentials. Together…
We confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth graded (not necessarily proper) gentle algebras form a complete derived invariant. Hence, we obtain a complete…
We show that the perfect derived categories of Iyama's $d$-dimensional Auslander algebras of type $\mathbb{A}$ are equivalent to the partially wrapped Fukaya categories of the $d$-fold symmetric product of the $2$-dimensional unit disk with…
This is an informal (and mostly conjectural) discussion of some aspects of Fukaya categories. We start by looking at exact symplectic manifolds which are obtained from a closed Calabi-Yau by removing a hyperplane section. We look at the…
We prove that every spherical object in the derived Fukaya category of a closed surface of genus at least two whose Chern character represents a non-zero Hochschild homology class is quasi-isomorphic to a simple closed curve equipped with a…
In this paper we study the localization of a derived category of a graded gentle algebra by a subcategory generated by a spherical band object. This object corresponds to a simple closed curve under the equivalence between the perfect…
A class of partially wrapped Fukaya categories in $T^* N$ are proven to be well defined and then studied. In the case of $N$ diffeomorphic to $\mathbb{R}^m \times \mathbb{T}^n$, it is shown that these categories provide homological mirrors…
Relative Fukaya categories are hard to construct. In this paper, we provide a very explicit construction in the case of punctured surfaces. The starting point is the gentle algebra $ \operatorname{Gtl} Q $ associated with a punctured…
Geometric models have emerged as an important tool in the representation theory of algebras. Surface models associated to gentle algebras have been particularly fruitful in advancing our understanding of their module and derived categories.…
We construct the Fukaya category of a closed surface equipped with an area form using only elementary (essentially combinatorial) methods. We also compute the Grothendieck group of its derived category.
In this paper, we construct a Fukaya category of any infinite type surface whose objects are gradient sectorial Lagrangians. This class of Lagrangian submanifolds is introduced by one of the authors in [Oh21b] which can serve as an object…
To a conical symplectic resolution with Hamiltonian torus action, Braden--Proudfoot--Licata--Webster associate a category O, defined using deformation quantization (DQ) modules. It has long been expected, though not stated precisely in the…
We compute the wrapped Fukaya category $\mathcal{W}(T^*S^1, D)$ of a cylinder relative to a divisor $D= \{p_1,\ldots, p_n\}$ of $n$ points, proving a mirror equivalence with the category of perfect complexes on a crepant resolution (over…
It follows from the work of Burban and Drozd arXiv:0905.1231 that for nodal curves $C$, the derived category of modules over the Auslander order $\mathcal{A}_C$ provides a categorical (smooth and proper) resolution of the category of…
Using Auroux's description of Fukaya categories of symmetric products of punctured surfaces, we compute the partially wrapped Fukaya category of the complement of $k+1$ generic hyperplanes in $\mathbb{CP}^n$, for $k \geq n$, with respect to…