相关论文: Presymplectic geometry and Liouville sectors with …

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…

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…

We prove the surprising fact that the infinity-category of stabilized Liouville sectors is a localization of an ordinary category of stabilized Liouville sectors and strict sectorial embeddings. From the perspective of homotopy theory, this…

We establish the continuous functoriality of wrapped Fukaya categories with respect to Liouville automorphisms, yielding a way to probe the homotopy type of the automorphism group of a Liouville sector. These methods prove Liouville and…

We construct an unwrapped Floer theory for bundles of Liouville sectors. In particular, we construct a compatible collection of unwrapped Fukaya categories of fibers of a Liouville bundle, and prove that the two natural constructions of…

To a simple polarized hyperplane arrangement (not necessarily cyclic) $\mathbb{V}$, one can associate a stopped Liouville manifold (equivalently, a Liouville sector) $\left(M(\mathbb{V}),\xi\right)$, where $M(\mathbb{V})$ is the complement…

Liouville domains are a special type of symplectic manifolds with boundary (they have an everywhere defined Liouville flow, pointing outwards along the boundary). Symplectic cohomology for Liouville domains was introduced by…

We develop an equivariant Lagrangian Floer theory for Liouville sectors that have symmetry of a Lie group $G$. Moreover, for Liouville manifolds with $G$-symmetry, we develop a correspondence theory to relate the equivariant Lagrangian…

We define a new class of symplectic objects called "stops", which roughly speaking are Liouville hypersurfaces in the boundary of a Liouville domain. Locally, these can be viewed as pages of a compatible open book. To a Liouville domain…

Liouville domains have become central objects in symplectic and contact geometry. However, the auxiliary data they involve --- namely, Liouville forms --- and the non-compactness of their completions generate some inconvenience. The notion…

The work of Oh and Park ([OP]) on the deformation problem of coisotropic submanifolds opened the possibility of studying a large and interesting class of foliations with some explicit geometric tools. These tools assemble into the structure…

By a Liouville structure on a symplectic manifold $(M, \omega)$ we mean a choice of symplectic potential: that is, a choice of one-form $\theta$ on $M$ such that ${\rm d} \theta = \omega$. We determine precisely all the automorphisms of a…

We introduce an $A_\infty$ map from the cubical chain complex of the based loop space of Lagrangian submanifolds with Legendrian boundary in a Liouville Manifold $C_{*}(\Omega_{L} \mathcal{L}\mathit{ag})$ to wrapped Floer cohomology of…

We construct the $L_\infty$ structure on symplectic cohomology of a Liouville domain, together with an enhancement of the closed--open map to an $L_\infty$ homomorphism from symplectic cochains to Hochschild cochains on the wrapped Fukaya…

The classical Arnold-Liouville theorem describes the geometry of an integrable Hamiltonian system near a regular level set of the moment map. Our results describe it near a nondegenerate singular level set: a tubular neighborhood of a…

Consider the wrapped Fukaya category W of a collection of exact Lagrangians in a Liouville manifold. Under a non-degeneracy condition implying the existence of enough Lagrangians, we show that natural geometric maps from the Hochschild…

In this paper we construct, in all odd complex dimensions, pairs of Liouville domains W_0 and W_1 which are diffeomorphic to the cotangent bundle of the sphere with one extra subcritical handle, but are not symplectomorphic. While W_0 is…

Given a collection of exact Lagrangians in a Liouville manifold, we construct a map from the Hochschild homology of the Fukaya category that they generate to symplectic cohomology. Whenever the identity in symplectic cohomology lies in the…

We prove that, for nice classes of infinite-dimensional smooth groups G, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of G. This yields a bridge between infinite-dimensional…

Given a strictly concave rational PL function $\phi$ on a complete $n$-dimensional fan $\Sigma$, we construct an exact symplectic structure of finite volume on $(\mathbb{C}^\times)^n$ and a family of functions $H_{\phi,\epsilon}$ called…