Alexandre Perrier
We study Lagrangian cobordism groups of oriented surfaces of genus greater than two. We compute the immersed oriented Lagrangian cobordism group of these surfaces. We show that a variant of this group, with relations given by unobstructed immersed Lagrangian cobordisms computes the Grothendieck group of the derived Fukaya category. The proof relies on an argument of Abouzaid.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
Lagrangian Realizations of Ribbon Cobordisms
该研究证明稳定化下光滑带状配边可由可分解拉格朗日配边实现，还定义拉格朗日配边的稳定化概念并表明其可用于寻找Legendrian链环间的新拉格朗日配边。
Lagrangian Quantum Homology for Lagrangian cobordism
我们将拉格朗日量子同调的定义推广到单调拉格朗日配边，并建立了它的一般代数性质。特别是，我们开发了一个相对版本的拉格朗日量子同源性相关的协边相对于其边界的一部分，并研究这种不变量的环境量子同源性的关系。
Exact Lagrangian cobordism and pseudo-isotopy
证明了在某些拓扑假设下，维数为$dim(W) >5$的精确拉格朗日配边$(W; L_{0}, L_{1})$是拉格朗日伪合痕.这个结果是Biran和Cornea提出的一个猜想的较弱形式，该猜想指出任何精确的拉格朗日配边都是拉格朗日悬挂的哈密顿同位素。
Lagrangian cobordism and metric invariants
我们引入新的伪度量空间的拉格朗日子流形的辛流形$(M,ω)$考虑相关领域的投影拉格朗日协边在$\mathbb{C} \times M$的“时间-能量平面”$\mathbb{C}$。我们调查这些伪度量的非退化属性，反映了拉格朗日配边的刚性和柔性方面。
Topology of (small) Lagrangian cobordisms
我们研究了以下辛拓扑中的定量现象：在许多情况下，如果拉格朗日配边足够小（在下面指定的意义上），那么它的拓扑在很大程度上取决于它的边界。这一原则使我们能够推导出几个同调的唯一性结果小拉格朗日配边。特别是，在小的假设下，我们证明了同调唯一性的类的拉格朗日配边，由Biran-Cornea的拉格朗日配边理论，诱导操作的一个版本的派生类。我们还建立了我们的结果和瓦西里耶夫的拉格朗日特征类理论之间的联系。大多数目前已知的拉格朗日配边构造在许多例子中产生小的拉格朗日配边。
Invariants of Lagrangian cobordisms via spectral numbers
我们扩展部分拉格朗日谱不变量包最近开发的Leclercq和Zapolsky的拉格朗日配边理论开发的Biran和角膜。这产生了一个非退化的拉格朗日“谱度量”的边界拉格朗日“cobordism度量”（最近推出的角膜和Shelukhin）从下面。它还产生了一个新的数值拉格朗日配边不变量以及计算某些渐近拉格朗日谱不变量明确的新方法。
Floer theory for Lagrangian cobordisms was developed by Biran and Cornea to study the triangulated structure of the derived Fukaya category of monotone symplectic manifolds. This paper explains how to use the language of stops to study Lagrangian cobordisms in Liouville manifolds and the associated exact triangles in the derived wrapped Fukaya category. Furthermore, we compute the cobordism groups of non-compact Riemann surfaces of finite type.
A note on the Lagrangian cobordism group of Weinstein sectors
本文证明了Weinstein扇区的Lagrangian配边群同构于其中间维奇异上同调群，并给出了Viterbo限制的几何描述。
A Seifert-van Kampen Theorem for Legendrian Submanifolds and Exact Lagrangian Cobordisms
我们证明了一个塞弗特-范坎彭定理的勒让德子流形和确切的拉格朗日配边，并用它来计算的DGA的变化所造成的关键勒让德环境手术。
Some cute applications of Lagrangian cobordisms towards examples in quantitative symplectic geometry
该研究利用拉格朗日余切给出构造改进辛挤压问题示例，还证明拉格朗日同痕的子流形是拉格朗日余切的，为定量辛几何研究提供新成果。
Floer theory for Lagrangian cobordisms
本文在Liouville流形接触化中为恰当拉格朗日配边建立交Floer同调，并借助正合序列研究其拓扑性质。
The Minimal Length of a Lagrangian Cobordism between Legendrians
为了研究Legendrian子流形之间的拉格朗日配边的刚性和柔性，我们研究了这种配边的最小长度，这是配边的非圆柱部分的$1$维度量.我们的主要工具是一组勒让德子流形，这是来自过滤版本的勒让德接触同调的实值容量。在拉格朗日配边的两端勒让德的容量之间的关系产生的配边长度的下界。我们适用于拉格朗日配边实现垂直膨胀（可能是任意短）和收缩（其长度有界以下）的能力。我们还研究了长度和多重配边的连接之间的相互作用，以及由Legendrian同位素的非平凡环导出的配边的长度。
A distance expanding flow on exact Lagrangian cobordism classes
给定一个精确辛流形$(M,dλ)$的精确拉格朗日$L$，Cornea和Shelukhin最近在$L$的精确拉格朗日配边类$\mathcal{L}(L)$上引入了一个显著的“配边度量”$d_c$.本文证明了$(M,dλ)$的Liouville流在$(\mathcal{L}(L),d_c)$上诱导了一个扩展配边距离的流。特别地，我们推导出$(\mathcal{L}(L),d_c)$有无穷大的直径时，刘维尔流是完整的。我们还讨论了（哈密顿和拉格朗日）霍费尔几何版本的结果。证明只使用初等微分几何。
Lagrangian cobordisms and K-theory of symplectic bielliptic surfaces
本文研究辛双椭圆曲面上弱正合拉格朗日G-膜的拉格朗日配边群，计算了热带拉格朗日生成的子群，并利用同调镜像对称性证明Fukaya范畴的Grothendieck群与配边群计算一致，进而提出热带拉格朗日生成整个配边群的猜想。
We study Lagrangian cobordisms with the tools provided by Lagrangian quantum homology. In particular, we develop the theory for the setting of Lagrangian cobordisms or Lagrangians with cylindrical ends in a Lefschetz fibration, and put the different versions of the quantum homology groups into relation by a long exact sequence. We prove various practical relations of maps in this long exact sequence and we extract invariants that generalize the notion of discriminants to Lagrangian cobordisms in Lefschetz fibrations. We prove results on the relation of the discriminants of the ends of a cobord…
Non-decomposable cobordisms via Lagrangian moves
本文通过拉格朗日图解移动构造勒让德结的协边，并利用稳定化与赖德迈斯特移动反转可分解协边，最终显式构造了从稳定化$m(9_{46})$结到稳定化平凡结的不可分解拉格朗日和谐性。
The fundamental group of a rigid Lagrangian cobordism
本文将Floer基本群的构造推广到单调拉格朗日情形，并利用它研究了两个拉格朗日子流形$L, L'\subset ( M, ω)$之间的拉格朗日配边$W\subset (\mathbb{C}\times M, ω_{st}\oplusω)$的基本群.我们证明了在自然条件下，包含$L,L'\hookrightarrow W$诱导满射映射$π_{1}(L)\twoheadrightarrowπ_{1}(W)$，$π_{1}(L')\twoheadrightarrowπ_{1}(W)$，并且当前面的映射是内射时，$W$是h-协边.
Lagrangian Cobordism I
本文讨论了拉格朗日子流形的配边性（在单调情形下），并将其构造为一个范畴，它以函子的方式与一个适当的（导）子流形范畴相联系。还讨论了障碍的协边的基础上的性质的拉格朗日量子同源性，关系到拉格朗日手术，以及非同位素，但协边拉格朗日的例子。这是我们2011年9月早期预印本的修订版。
Open Gromov-Witten invariants in genus zero and Lagrangian cobordisms
针对任意闭辛流形和嵌入的相对自旋Lagrangian子流形，利用边界上链构造了亏格零的开放Gromov-Witten不变量，证明了开放WDVV关系及其对近复结构和Hamilton同痕的无关性，并建立了配边Lagrangian之间的不变量关系。
Unobstructed Lagrangian cobordism groups of surfaces
本文研究了亏格 $g \geq 2$ 的闭辛曲面的无阻碍浸入拉格朗日配边群，基于 Abouzaid 和 Perrier 的工作计算了该群，并证明其同构于曲面的导出 Fukaya 范畴的 Grothendieck 群，证明中利用二维拓扑技术构造了不界定特定全纯多边形的配边。
Obstructions to the Existence and Squeezing of Lagrangian Cobordisms
利用生成族理论定义了在$\mathbb{R}^{2n}$的平行超平面中两个$(n-1)$维子流形之间存在拉格朗日配边的定性和定量障碍.定性地，这些能力表明，例如，在$\mathbb R^4$有没有拉格朗日配边两个$\infty$形曲线之间的负交叉时，下端是“较小的”。定量地说，当拉格朗日球的边界位于$\mathbb{R}^{2n}$的超平面中时，边界的容量对拉格朗日球可以被挤压到的矩形柱的大小给出限制。
Let $Λ, Λ'$ be a pair of closed Legendrian submanifolds in a closed contact manifold $(Y, ξ= Ker(α))$ related by a Legendrian cobordism $W\subset (\mathbb{C}\times Y, \tildeξ=Ker(-y dx +α))$. In this note, we show that in the hypertight setting, if $Λ$ intersects a closed, weakly exact or monotone pre-Lagrangian $P\subset Y$ for reasons of Floer homology, then so does $Λ'$.
In this paper we study the interplay between Lagrangian cobordisms and stability conditions. We show that any stability condition on the derived Fukaya category $D\mathcal{F}uk(M)$ of a symplectic manifold $(M,ω)$ induces a stability condition on the derived Fukaya category of Lagrangian cobordisms $D\mathcal{F}uk(\mathbb{C} \times M)$. In addition, using stability conditions, we provide general conditions under which the homomorphism $Θ: Ω_{Lag}(M)\to K_0(D\mathcal{F}uk(M))$, introduced by Biran and Cornea, is an isomorphism. This yields a better understanding of how stability conditions affe…
For $1$-dimensional Legendrian submanifolds of $1$-jet spaces, we extend the functorality of the Legendrian contact homology DG-algebra (DGA) from embedded exact Lagrangian cobordisms, as in \cite{EHK}, to a class of immersed exact Lagrangian cobordisms by considering their Legendrian lifts as conical Legendrian cobordisms. To a conical Legendrian cobordism $Σ$ from $Λ_-$ to $Λ_+$, we associate an immersed DGA map, which is a diagram $$\alg(Λ_+) \stackrel{f}{\rightarrow} \alg(Σ) \stackrel{i}{\hookleftarrow} \alg(Λ_-), $$ where $f$ is a DGA map and $i$ is an inclusion map. This construction giv…
Wall-crossing from Lagrangian Cobordisms
本文将 Biran-Cornea 的拉格朗日配边理论推广到珠状 Floer 上同调与无阻碍配边，构造首个两端非平凡等价，并解释墙-crossing 中的瞬子修正。
The Lagrangian cobordism group of $T^2$
计算了标准辛2-环面的拉格朗日配边群，并证明了它与其导出的辛2-环面范畴的Grothendieck群同构。证明使用同调镜像对称的2-环面。
We construct a product on the Floer complex associated to a pair of Lagrangian cobordisms. More precisely, given three exact transverse Lagrangian cobordisms in the symplectization of a contact manifold, we define a map $\mathfrak{m}_2$ by a count of rigid pseudo-holomorphic disks with boundary on the cobordisms and having punctures asymptotic to intersection points and Reeb chords of the negative Legendrian ends of the cobordisms. More generally, to a $(d+1)$-tuple of exact transverse Lagrangian cobordisms we associate a map $\mathfrak{m}_d$ such that the family $(\mathfrak{m}_d)_{d\geq1}$ ar…
We investigate the interactions between the Legendrian satellite construction and the existence of exact, orientable Lagrangian cobordisms between Legendrian knots. Given Lagrangian cobordisms between two Legendrian knots and between two Legendrian tangles, we construct a Lagrangian cobordism between Legendrian satellites of the knots by the closures of the tangles, with extra twists on both the top and the bottom satellite to compensate for the genus of the cobordism. If the original cobordisms were decomposable, then a decomposable cobordism between satellites exists as well, again with extr…
A note on Lagrangian cobordisms between Legendrian submanifolds of R^{2n+1}
本文研究了R^{2n+1}中两个闭的可定向勒让德子流形之间的嵌入拉格朗日配边关系。更确切地说，我们调查的行为的Thurston-Bennequin数和（线性化）Legendrian接触下的关系。关于Thurston-Bennequin数的结果可以被认为是Chantraine的结果的推广，当n = 1时，Chantraine的结果成立。另外，我们给出了几种拉格朗日配边的构造，并证明了在R^{2n+1}中存在无穷多对正合拉格朗日配边和非成对勒让德同位素勒让德n环面.
Non-decomposable Lagrangian cobordisms between Legendrian knots
给定\(g>0\)，构建一族标准接触三维球面中（稳定）勒让德纽结间亏格为\(g\)的不可分解拉格朗日配边，用利文斯顿估计法阻碍可分解性。
In this paper, we present new obstructions to the existence of Lagrangian cobordisms in $\mathbb{R}^4$ that depend only on the enriched knot diagrams of the boundary knots or links, using holomorphic curve techniques. We define enriched knot diagrams for generic smooth links. The existence of Lagrangian cobordisms gives a well-defined transitive relation on equivalence classes of enriched knot diagrams that is a strict partial order when restricted to exact enriched knot diagrams To establish obstructions we study $1$-dimensional moduli spaces of holomorphic disks with corners that have bounda…
Given an exact symplectic manifold M and a support Lagrangian Λ, we construct an infinity-category Lag, which we conjecture to be equivalent (after specialization of the coefficients) to the partially wrapped Fukaya category of M relative to Λ. Roughly speaking, the objects of Lag are Lagrangian branes inside of M x T*(R^n), for large n, and the morphisms are Lagrangian cobordisms that are non-characteristic with respect to Λ. The main theorem of this paper is that Lag is a stable infinity-category, so that its homotopy category is triangulated, with mapping cones given by an elementary constr…
We obtain upper and lower bounds for the relative Gromov width of Lagrangian cobordisms between Legendrian submanifolds. Upper bounds arise from the existence of $J$-holomorphic disks with boundary on the Lagrangian cobordism that pass through the center of any given symplectically embedded ball. The areas of these disks --- and hence the sizes of these balls --- are controlled by a real-valued fundamental capacity, a quantity derived from the algebraic structure of filtered linearized Legendrian Contact Homology of the Legendrian at the top of the cobordism. Lower bounds come from explicit co…
Lagrangian Cobordisms via Generating Families: Constructions and Geography
勒让德子流形之间的嵌入拉格朗日配边是由采用生成族技术的合痕、旋转和手柄连接构造产生的。此外，任何具有生成族的Legendrian都具有具有相容生成族的浸入拉格朗日填充。这些构造在几个方向上都有应用，特别是在一个非经典的地理问题上：任何满足对偶条件的分次群都可以被实现为R^{2n+1}中连通勒让德子流形的生成族同调，或者在n至少为2的紧致n-流形的1-jet空间中。
We define a unital $A_\infty$-category whose objects are exact Lagrangian cobordisms in the symplectization of $Y=P\times\mathbb{R}$, with negative cylindrical ends over Legendrians equipped with augmentations. The morphism spaces are given in terms of Floer complexes $Cth_+(Σ_0,Σ_1)$ which are versions of the Rabinowitz Floer complex defined by Symplectic Field Theory (SFT) techniques.
Khovanov homology and Lagrangian cobordisms
本文探讨了Khovanov同调与可分解Lagrangiancobordisms之间的关系，通过过滤不变量提供了部分答案及障碍条件。
Noncommutativity of monotone Lagrangian cobordisms
本文在CP^7中构造了从L到(L_1, L_2)的单调自旋拉格朗日配边，证明其反向配边不存在，揭示了单调拉格朗日配边的非交换性。
Lagrangian $k$-surgery modifies an immersed Lagrangian submanifold by topological $k$-surgery while removing a self-intersection. Associated to a $k$-surgery is a Lagrangian surgery trace cobordism. We prove that every Lagrangian cobordism is exactly homotopic to a concatenation of suspension cobordisms and Lagrangian surgery traces. This exact homotopy can be chosen with as small Hofer norm as desired. Furthermore, we show that each Lagrangian surgery trace bounds a holomorphic teardrop pairing the Morse cochain associated with the handle attachment to the Floer cochain generated by the self-…
A note on exact Lagrangian cobordisms with disconnected Legendrian ends
我们在本说明中提供了两个相关的例子拉格朗日配边。第一个例子给出了两个精确的拉格朗日子流形，不能组成一个精确的方式。第二个是一个例子，一个确切的拉格朗日配边论上的所有原始的刘维形式是不恒定的负端，使积极的结束是一个稳定，而负端承认增广。这些例子强调了[6]中精确拉格朗日配边定义的第（i）点。为了提供这样的例子，我们构造拉格朗日浸入与单二重点使用一个明确的模型和解释这种拉格朗日协边从Hopf链接。
Lagrangian cobordisms between Legendrian knots arise in Symplectic Field Theory and impose an interesting and not well-understood relation on Legendrian knots. There are some known "elementary" building blocks for Lagrangian cobordisms that are smoothly the attachment of $0$- and $1$-handles. An important question is whether every pair of non-empty Legendrians that are related by a connected Lagrangian cobordism can be related by a ribbon Lagrangian cobordism, in particular one that is "decomposable" into a composition of these elementary building blocks. We will describe these and other combi…
Lagrangian cobordism and shadow distance in Tamarkin category
本文利用层微局部理论构造精确 Lagrangian cobordism 的层量子化，证明交错距离受 shadow distance 约束，并由此通过能量代价估计得到 Lagrangian 交点的刚性结果。
We prove that the LOSS and GRID invariants of Legendrian links in knot Floer homology behave in certain functorial ways with respect to decomposable Lagrangian cobordisms in the symplectization of the standard contact structure on $\mathbb{R}^3$. Our results give new, computable, and effective obstructions to the existence of such cobordisms.
Legendrian knots and exact Lagrangian cobordisms
介绍了由辛域论导出的具有圆柱勒让德端点的精确拉格朗日配边的构造，并研究了它们的不变量。由一个正合辛流形$X$和一个正合拉格朗日协边$L\subset X$组成的一对$(X,L)$在正、负两端与Legendrian链环$Λ_+$和$Λ_-$上的柱面一致，诱导出一个从$Λ_+$的Legendrian接触同调DGA到$Λ_-$的Legendrian接触同调DGA的微分分次代数（DGA）映射.我们给出了某些对$(X,L)$的DGA映射的梯度流树描述，这反过来又产生了对初等配边的配边映射的纯组合描述，即，对应于勒让德结的某些局部修改的配边。作为一个应用程序，我们找到确切的拉格朗日曲面，填补了一个固定的勒让德链接，并没有通过确切的拉格朗日曲面的同位素。
Algebraic Lagrangian cobordisms, flux and the Lagrangian Ceresa cycle
本文引入代数拉格朗日配边等价关系，并借助热带与辛通量证明拉格朗日Ceresa圈在对应配边群中非挠，从而给出Ceresa圈非挠性的辛镜像类比。
The Fukaya category pairs with Lagrangian cobordisms exactly
我们证明了拉格朗日配边的O-category和O-category之间的配对是关于映射锥的。这是朝着构造一个提升到谱水平（在稳定同伦理论的意义上）的类的又一步。作为推论，我们证明了我们以前工作中从配边群到Floer上同调的映射提升到谱的水平，并且我们还恢复了Biran和Cornea关于我们称之为“垂直领”配边群的一些结果.
We study a cylindrical Lagrangian cobordism group for Lagrangian torus fibres in symplectic manifolds which are the total spaces of smooth Lagrangian torus fibrations. We use ideas from family Floer theory and tropical geometry to obtain both obstructions to and constructions of cobordisms; in particular, we give examples of symplectic tori in which the cobordism group has no non-trivial cobordism relations between pairwise distinct fibres, and ones in which the degree zero fibre cobordism group is a divisible group. The results are independent of but motivated by mirror symmetry, and a relati…
We introduce a new type of duality structure for $A_\infty$-categories called a relative weak Calabi-Yau pairing which generalizes Kontsevich and Soibelman's notion of a weak (proper) Calabi-Yau structure. We prove the existence of a relative weak Calabi-Yau pairing on Biran and Cornea's Fukaya category of Lagrangian cobordisms $\mathcal{F}uk_{\mathit{cob}}(\mathbb{C}\times M)$. Here $M$ is a symplectic manifold which is closed or tame at infinity. This duality structure on $\mathcal{F}uk_{\mathit{cob}}(\mathbb{C}\times M)$ extends the relative Poincaré duality satisfied by Floer complexes for…
Double-point enhanced GRID invariants and Lagrangian cobordisms
本文在双点增强网格同调中构造勒让德链环不变量，并用其阻碍标准接触三维空间辛化中的可分解拉格朗日配边。
We prove that a real Lagrangian submanifold in a closed symplectic manifold is unique up to cobordism. We then discuss the classification of real Lagrangians in $\mathbb{C} P^2$ and $S^2\times S^2$. In particular, we show that a real Lagrangian in $\mathbb{C} P^2$ is unique up to Hamiltonian isotopy and that a real Lagrangian in $S^2\times S^2$ is either Hamiltonian isotopic to the antidialgonal sphere or Lagrangian isotopic to the Clifford torus.
In simply-connected cotangent bundles, exact Lagrangian cobordisms are h-cobordisms
该研究在单连通余切丛中证明了精确拉格朗日cobordism与h-cobordism之间的等价关系，利用阿布扎伊德-克拉格定理实现了基础代数拓扑学的结论。
Non-Orientable Lagrangian Cobordisms between Legendrian Knots
在标准接触$3$ -空间$\mathbb R \times \mathbb R^3$的辛化中，已知勒让德结与其自身之间的可定向拉格朗日配边，也称为勒让德结的可定向拉格朗日内配边，必须具有亏格$0$。我们证明了任何勒让德纽结都有不可定向的拉格朗日内协边，并且这种不可定向的拉格朗日内协边的横截亏格必须是$4$的正倍数。更严格的精确，不可定向的拉格朗日内配边不存在于任何精确可填充的勒让德纽结，但存在于任何稳定的勒让德纽结。此外，由精确的，不可定向的拉格朗日配边定义的稳定勒让德结的集合上的关系是对称的，并定义了一个等价关系，一个对比的非对称关系定义的可定向的拉格朗日配边。
Lagrangian cobordism in Lefschetz fibrations
给定一个辛流形$(M^{2n},ω)$，我们研究了Lagrange协边$V\subset E$，其中$E$是以$M$为类纤维的Lefschetz纤维化的全空间.我们证明了这些配边在适当的派生类的生成结果。作为推论，我们分析了由这些配边诱导的拉格朗日子流形$L\subset M$之间的关系。这导致了一个统一的治疗-和推广-的两种类型的关系之间的拉格朗日子流形的$M$，以前确定的文献中：那些相关的Dehn扭曲发现的赛德尔和关系引起的协边在平凡的辛纤维化中描述我们以前的工作。
We prove that if L_0 and L_1 are exact branes intersecting in precisely one point, then there exists a fiber sequence in the infinity-category of Lagrangian cobordisms consisting of L_0, L_1, and a surgery of L_0 with L_1. By combining this with the exact functor from [Tan], we find analogues of results of Biran and Cornea in the wrapped and exact setting.
Lagrangian Zigzag Cobordisms
本文研究了标准接触三维空间中Legendrian纽结基于拉格朗日之字形配边的等价关系，将其与光滑配边和拉格朗日配边进行比较，分析了相应度量幺半群的结构，并探讨了其与纽结非经典不变量的联系。
For $X = \mathbb{P}^n$ the Euler sequence is given by $$ 0 \rightarrow Ω^1_{\mathbb{P}^n} \rightarrow \mathcal{O}_{\mathbb{P}^n}^{n+1}(-1) \rightarrow \mathcal{O}_{\mathbb{P}^n} \rightarrow 0 $$ We describe the Lagrangian cobordism corresponding to this sequence via mirror symmetry, in the sense of Biran-Cornea. In particular, we describe the mirror Lagrangian of the cotangent sheaf $Ω^1_{\mathbb{P}^n} \in \mathcal{D}^b(\mathbb{P}^n)$ in the mirror Fukaya category $Fuk(U_Δ)$.
Lagrangian cobordism of positroid links
本研究针对复格拉斯曼流形正半单形层的偏序，证明其可通过精确拉格朗日余挠实现辛解释，建立代数几何层结构与辛拓扑余挠的联系。
We prove that Lagrangian cocores and Lagrangian linking disks of a stopped Weinstein manifold generate the Lagrangian cobordism infinity-category. As a geometric consequence, we see that any brane (after stabilization) admits a Lagrangian cobordism to a disjoint union of some standard collection of branes (cocores, linking disks, and a zero object). For example, when our stopped Weinstein manifold is a point stopped by itself, we find that any exact brane in Euclidean space admits a Lagrangian cobordism to a disjoint union of cotangent fibers and a zero object. (This is a stronger statement th…
Spectral GRID invariants and Lagrangian cobordisms
本研究证明Legendrian链环的滤过GRID不变量及其谱序列不变量可阻碍$\u211d^3$标准切触结构辛化中的可分解拉格朗日配边，强化了已有相关研究结果。
Dehn twists exact sequences through Lagrangian cobordism
本文介绍了以下新的内容：（1）对Lagrange手术理论的部分修正;（2）在乘积辛流形上构造Lagrange配边;（3）将Biran-Cornea Lagrange配边理论推广到浸入范畴.其结果是，我们表现出赛德尔的确切序列（拉格朗日版本和symplectomorphism版本），以及Wehrheim-Woodward的家庭德恩扭曲序列（包括余维-1的情况下，在文献中丢失）作为我们的手术/协边结构的后果。此外，我们还得到了由Dehn扭曲诱导的类范畴沿拉格朗日$\mathbb{RP}^n$，$\mathbb{CP}^n$和$\mathbb{HP}^n$的自等价表达式，它与Huybrechts-Thomas关于$\mathbb{CP}^n$模连通映射的镜像预言相匹配.我们还证明了在$ADE$型Milnor纤维中，任何辛同胚的Dehn扭曲的分裂生成。
On Lagrangian cobordisms and the Chekanov-Eliashberg DGA
本文研究了拉格朗日cobordisms对Legendrian端点Chekanov-Eliashberg DGA的诱导映射，并证明其在拉格朗日同伦下的不变性及更高阶乘积结构的性质。
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。