Related papers: On the abstract wrapped Floer setups
We construct a stable infinity category with objects flow categories and morphisms flow bimodules; our construction has many flavors, related to a choice of bordism theory, and we discuss in particular framed bordism and the bordism theory…
Suppose one has found a non-empty sub-category $\mathcal{A}$ of the Fukaya category of a compact Calabi-Yau manifold $X$ which is homologically smooth in the sense of non-commutative geometry, a condition intrinsic to $\mathcal{A}$. Then,…
In this paper, we prove that the derived Rabinowitz Fukaya category of a Liouville domain $M$ of dimension $2n$ is $(n-1)$-Calabi--Yau assuming the wrapped Fukaya category of $M$ admits an at most countable set of Lagrangians that generate…
Let $Ham (M,\omega ) $ denote the Frechet Lie group of Hamiltonian symplectomorphisms of a monotone symplectic manifold $(M, \omega) $. Let $NFuk (M, \omega)$ be the $A _{\infty} $-nerve of the Fukaya category $Fuk (M, \omega)$, and let…
This paper describes constructions in homological algebra that are part of a strategy whose goal is to understand and classify symplectic mapping tori. More precisely, given a dg category and an auto-equivalence, satisfying certain…
We outline a proposal for a $2$-category $\mathrm{Fuet}_M$ associated to a hyperk\"ahler manifold $M$, which categorifies the subcategory of the Fukaya category of $M$ generated by complex Lagrangians. Morphisms in this $2$-category are…
We define enumerative invariants associated to a hybrid Gauged Linear Sigma Model. We prove that in the relevant special cases, these invariants recover both the Gromov-Witten type invariants defined by Chang-Li and Fan-Jarvis-Ruan using…
We introduce a new package of Floer data of $\lambda$-sectorial almost complex structures $J$ and sectorial Hamiltonians $H$ on the Liouville sectors introduced by Ganatra-Pardon-Shende the pairs of which are amenable to the maximum…
Seidel introduced the notion of a Fukaya category `relative to an ample divisor', explained that it is a deformation of the Fukaya category of the affine variety that is the complement of the divisor, and showed how the relevant deformation…
Let $M$ be a Liouville 6-manifold which is the smooth fiber of a Lefschetz fibration on $\mathbb{C}^4$ constructed by suspending a Lefschetz fibration on $\mathbb{C}^3$. We prove that for many examples including stabilizations of Milnor…
To a noncompact orientable surface with no closed boundary, we associate the sum of Fukaya categories of (Liouville sectors associated to) its symmetric powers. We construct sectorial covers with the combinatorics of the bar resolution to…
Inspired by Segal-Stolz-Teichner project for geometric construction of elliptic (tmf) cohomology, and ideas of Floer theory and of Hopkins-Lurie on extended TFT's, we geometrically construct some $Ring$-valued representable cofunctors on…
We study the space of $A_\infty$-natural transformations between braiding functors acting on the Fukaya category associated to the Coulomb branch $\mathcal{M}(\bullet,1)$ of the $\mathfrak{sl}_2$ quiver gauge theory. We compute all…
We study the Rouquier dimension of wrapped Fukaya categories of Liouville manifolds and pairs, and apply this invariant to various problems in algebraic and symplectic geometry. On the algebro-geometric side, we introduce a new method based…
We survey various aspects of Floer theory and its place in modern symplectic geometry, from its introduction to address classical conjectures of Arnold about Hamiltonian diffeomorphisms and Lagrangian submanifolds, to the rich algebraic…
These are notes from a 2010 talk. They concern possible ways in which Fukaya categories might be considered as "local", which means glued together from simpler pieces in a loosely sheaf-theoretic sense. As the title suggests, this is purely…
Given a punctured Riemann surface with a pair-of-pants decomposition, we compute its wrapped Fukaya category in a suitable model by reconstructing it from those of various pairs of pants. The pieces are glued together in the sense that the…
We introduce a category of Kuranishi presentations, whose objects are a variant of the Kuranishi structures introduced by Fukaya and Ono, and which can be seen as a refinement of the version studied by Pardon. We then formulate the notion…
We develop a local-to-global formalism for constructing Calabi-Yau structures for global sections of constructible sheaves or cosheaves of categories. The required data - an isomorphism of the sheafified Hochschild homology with the…
In this paper, we define a family of categories for each Liouville manifold, which is an enhanced version of the category first introduced by Tamarkin. Using our categories, for any (possibly non-exact immersed) Lagrangian brane, we develop…