Related papers: Open-closed Deligne-Mumford field theories: constr…
We construct global Kuranishi charts for moduli spaces of pseudo-holomorphic maps of arbitrary genus with boundary on an embedded Lagrangian submanifold. We then build the geometric foundations required for obtaining compatible chain-level…
We construct open-closed maps on various versions of Hochschild and cyclic homology of the Fukaya $A_\infty$ algebra of a Lagrangian submanifold modeled on differential forms. The $A_\infty$ algebra may be curved. Properties analogous to…
I classify all cohomological 2D field theories based on a semi-simple complex Frobenius algebra A. They are controlled by a linear combination of kappa-classes and by an extension datum to the Deligne-Mumford boundary. Their effect on the…
This is the first of two papers which construct a purely algebraic counterpart to the theory of Gromov-Witten invariants (at all genera). These Gromov-Witten type invariants depend on a Calabi-Yau A-infinity category, which plays the role…
This paper proposes a framework to show that the Fukaya category of a symplectic manifold $X$ determines the open Gromov-Witten invariants of Lagrangians $L \subset X$. We associate to an object in an $A_\infty$-category an extension of the…
Consider the differential forms $A^*(L)$ on a Lagrangian submanifold $L \subset X$. Following ideas of Fukaya-Oh-Ohta-Ono, we construct a family of cyclic unital curved $A_\infty$ structures on $A^*(L),$ parameterized by the cohomology of…
Categorical enumerative invariants of a Calabi-Yau category, encoded as the partition function of the associated closed string field theory (SFT), conjecturally equal Gromov-Witten invariants when applied to Fukaya categories. Part of this…
We give a classification of open Klein topological conformal field theories in terms of Calabi-Yau $A_\infty$-categories endowed with an involution. Given an open Klein topological conformal field theory, there is a universal open-closed…
In this expository manuscript, we review the construction of Gromov-Witten virtual fundamental class via FOOO's theory of Kuranishi structures for moduli spaces of pseudo-holomorphic maps defined on closed Riemann surfaces. We consider…
String theory on D-brane backgrounds is open-closed string theory. Given the relevance of this fact, we give details and elaborate upon our earlier construction of oriented open-closed string field theory. In order to incorporate explicitly…
In this article, we establish a connection between two models for $r$-spin structures on surfaces: the marked PLCW decompositions of Novak and Runkel-Szegedy, and the structured graphs of Dyckerhoff-Kapranov. We use these models to describe…
We construct a lax monoidal Topological Quantum Field Theory that computes Deligne-Hodge polynomials of representation varieties of the fundamental group of any closed manifold into any complex algebraic group $G$. As byproduct, we obtain…
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…
A geometric first-order axiomatization of differentially closed fields of characteristic zero with several commuting derivations, in the spirit of Pierce-Pillay, is formulated in terms of a relative notion of prolongation for Kolchin-closed…
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. Under certain conditions,…
We investigate a classical open-closed string field theory whose open string sector is given by boundary string field theory. The open-closed interaction is introduced by the overlap of a boundary state with a closed string field. With the…
Let $L\subset X$ be a not necessarily orientable relatively $Pin$ Lagrangian submanifold in a symplectic manifold $X$. We construct a family of cyclic unital curved $A_\infty$ structures on differential forms on $L$ with values in the local…
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…
By studying spaces of flow graphs in a closed oriented manifold, we construct operations on its cohomology, parametrized by the homology of the moduli spaces of compact Riemann surfaces with boundary marked points. We show that the…
We study open-closed orbifold Gromov-Witten invariants of 3-dimensional Calabi-Yau smooth toric Deligne-Mumford (DM) stacks (with possibly non-trivial generic stabilizers and semi-projective coarse moduli spaces) relative to Lagrangian…