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Journal of Symplectic Geometry最新文献

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On the lower bounds of the $L^2$-norm of the Hermitian scalar curvature 在厄米标量曲率的L^2范数的下界上
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2017-02-06 DOI: 10.4310/jsg.2020.v18.n2.a5
Julien Keller, Mehdi Lejmi
{"title":"On the lower bounds of the $L^2$-norm of the Hermitian scalar curvature","authors":"Julien Keller, Mehdi Lejmi","doi":"10.4310/jsg.2020.v18.n2.a5","DOIUrl":"https://doi.org/10.4310/jsg.2020.v18.n2.a5","url":null,"abstract":"On a pre-quantized symplectic manifold, we show that the symplectic Futaki invariant, which is an obstruction to the existence of constant Hermitian scalar curvature almost-K\"ahler metrics, is actually an asymptotic invariant. This allows us to deduce a lower bound for the L^2-norm of the Hermitian scalar curvature as obtained by S. Donaldson cite{Don} in the K\"ahler case.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2017-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72857861","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
Existence of noncontractible periodic orbits of Hamiltonian systems separating two Lagrangian tori on $T^{*} mathbb{T}^n$ with application to nonconvex systems $T^{*} mathbb{T}^n$上分离两个拉格朗日环面哈密顿系统不可收缩周期轨道的存在性及其在非凸系统上的应用
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2017-01-01 DOI: 10.4310/JSG.2017.V15.N3.A10
Jinxin Xue
{"title":"Existence of noncontractible periodic orbits of Hamiltonian systems separating two Lagrangian tori on $T^{*} mathbb{T}^n$ with application to nonconvex systems","authors":"Jinxin Xue","doi":"10.4310/JSG.2017.V15.N3.A10","DOIUrl":"https://doi.org/10.4310/JSG.2017.V15.N3.A10","url":null,"abstract":"In this paper, we show the existence of non-contractible periodic orbits in Hamiltonian systems defined on T ∗Tn separating two Lagrangian tori under a certain cone assumption. Our result gives a positive answer to a question of Polterovich in [P]. As an application, we find periodic orbits in almost all the homotopy classes on a dense set of energy levels in Lorentzian type mechanical Hamiltonian systems defined on T ∗T2. This solves a problem of Arnold in [A].","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"44 1","pages":"905-936"},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79362673","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Lagrangian submanifolds at infinity and their parametrization 无穷远处的拉格朗日子流形及其参数化
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2017-01-01 DOI: 10.4310/JSG.2017.V15.N4.A1
S. Coriasco, R. Schulz
{"title":"Lagrangian submanifolds at infinity and their parametrization","authors":"S. Coriasco, R. Schulz","doi":"10.4310/JSG.2017.V15.N4.A1","DOIUrl":"https://doi.org/10.4310/JSG.2017.V15.N4.A1","url":null,"abstract":"In this paper, we study a class of Lagrangian submanifolds which may be viewed as intersecting at infinity. They are objects natu-rally associated with a class of tempered oscillatory integrals. In this context, we prove the adapted versions of the classical the-orems, such as parametrization results, as well as equivalence of phase functions.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"69 1","pages":"937-982"},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80347789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 9
On non-contractible periodic orbits of symplectomorphisms 关于辛形态的不可收缩周期轨道
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2017-01-01 DOI: 10.4310/JSG.2017.V15.N3.A3
Marta Batoréo
{"title":"On non-contractible periodic orbits of symplectomorphisms","authors":"Marta Batoréo","doi":"10.4310/JSG.2017.V15.N3.A3","DOIUrl":"https://doi.org/10.4310/JSG.2017.V15.N3.A3","url":null,"abstract":"We prove the existence of infinitely many periodic points of symplectomorphisms isotopic to the identity if they admit at least one (non-contractible) hyperbolic periodic orbit and satisfy some condition on its flux. The obtained periodic points correspond to periodic orbits whose free homotopy classes are formed by iterations of the hyperbolic periodic orbit. Our result is proved for a certain class of closed symplectic manifolds and the main tool we use is a variation of Floer theory for non-contractible periodic orbits and symplectomorphisms, the Floer–Novikov theory. For a certain class of symplectic manifolds, the theorem generalizes the main results proved for Hamiltonian diffeomorphisms in [16] and for symplectomorphisms and contractible orbits in [2].","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"27 1","pages":"687-717"},"PeriodicalIF":0.7,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82652653","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 8
Squared Dehn twists and deformed symplectic invariants 平方Dehn扭曲和变形辛不变量
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2016-09-27 DOI: 10.4310/jsg.2021.v19.n5.a5
Kyler Siegel
{"title":"Squared Dehn twists and deformed symplectic invariants","authors":"Kyler Siegel","doi":"10.4310/jsg.2021.v19.n5.a5","DOIUrl":"https://doi.org/10.4310/jsg.2021.v19.n5.a5","url":null,"abstract":"We establish an infinitesimal version of fragility for squared Dehn twists around even dimensional Lagrangian spheres. The precise formulation involves twisting the Fukaya category by a closed two-form or bulk deforming it by a half-dimensional cycle. As our main application, we compute the twisted and bulk deformed symplectic cohomology of the subflexible Weinstein manifolds constructed in cite{murphysiegel}.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"17 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2016-09-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85196083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 5
Picard groups of $b$-symplectic manifolds b -辛流形的Picard群
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2016-09-17 DOI: 10.4310/JSG.2021.v19.n3.a6
J. Villatoro
{"title":"Picard groups of $b$-symplectic manifolds","authors":"J. Villatoro","doi":"10.4310/JSG.2021.v19.n3.a6","DOIUrl":"https://doi.org/10.4310/JSG.2021.v19.n3.a6","url":null,"abstract":"We compute the Picard group of a stable b-symplectic manifold $M$ by introducing a collection of discrete invariants $mathfrak{Gr}$ which classify $M$ up to Morita equivalence.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"26 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2016-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73735161","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Contact categories of disks 磁盘的接触类别
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2016-08-30 DOI: 10.4310/jsg.2022.v20.n3.a3
K. Honda, Yin Tian
{"title":"Contact categories of disks","authors":"K. Honda, Yin Tian","doi":"10.4310/jsg.2022.v20.n3.a3","DOIUrl":"https://doi.org/10.4310/jsg.2022.v20.n3.a3","url":null,"abstract":"In the first part of the paper we associate a pre-additive category $mathcal{C}(Sigma)$ to a closed oriented surface $Sigma$, called the {em contact category} and constructed from contact structures on $Sigmatimes[0,1]$. There are also $mathcal{C}(Sigma,F)$, where $Sigma$ is a compact oriented surface with boundary and $Fsubset partialSigma$ is a finite oriented set of points which bounds a submanifold of $partialSigma$, and universal covers $widetilde{mathcal{C}}(Sigma)$ and $widetilde{mathcal{C}}(Sigma,F)$ of $mathcal{C}(Sigma)$ and $mathcal{C}(Sigma,F)$. In the second part of the paper we prove that the universal cover of the contact category of a disk admits an embedding into its \"triangulated envelope.\"","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2016-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78867508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Symplectically replacing plumbings with Euler characteristic $2 : 4$‑manifolds 用欧拉特征$2 :4$流形辛替换管道
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2016-08-17 DOI: 10.4310/jsg.2020.v18.n5.a4
Jonathan Simone
{"title":"Symplectically replacing plumbings with Euler characteristic $2 : 4$‑manifolds","authors":"Jonathan Simone","doi":"10.4310/jsg.2020.v18.n5.a4","DOIUrl":"https://doi.org/10.4310/jsg.2020.v18.n5.a4","url":null,"abstract":"We introduce new symplectic cut-and-paste operations that generalize the rational blowdown. In particular, we will define $k$-replaceable plumbings to be those that, heuristically, can be symplectically replaced by Euler characteristic $k$ 4-manifolds. We will then classify 2-replaceable linear plumbings, construct 2-replaceable plumbing trees, and use one such tree to construct a symplectic exotic $mathbb{C}P^2#6overline{mathbb{C}P^2}$.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"1654 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2016-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86392717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Differential forms, Fukaya $A_infty$ algebras, and Gromov–Witten axioms 微分形式，Fukaya $A_infty$代数，和Gromov-Witten公理
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2016-08-03 DOI: 10.4310/JSG.2022.v20.n4.a5
Jake Solomon, Sara B. Tukachinsky
{"title":"Differential forms, Fukaya $A_infty$ algebras, and Gromov–Witten axioms","authors":"Jake Solomon, Sara B. Tukachinsky","doi":"10.4310/JSG.2022.v20.n4.a5","DOIUrl":"https://doi.org/10.4310/JSG.2022.v20.n4.a5","url":null,"abstract":"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 $X$ relative to $L.$ The family of $A_infty$ structures satisfies properties analogous to the axioms of Gromov-Witten theory. Our construction is canonical up to $A_infty$ pseudoisotopy. We work in the situation that moduli spaces are regular and boundary evaluation maps are submersions, and thus we do not use the theory of the virtual fundamental class.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"50 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2016-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91357138","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 6
The diffeomorphism type of symplectic fillings 辛填充的微分同胚类型
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2016-07-12 DOI: 10.4310/jsg.2019.v17.n4.a1
Kilian Barth, H. Geiges, Kai Zehmisch
{"title":"The diffeomorphism type of symplectic fillings","authors":"Kilian Barth, H. Geiges, Kai Zehmisch","doi":"10.4310/jsg.2019.v17.n4.a1","DOIUrl":"https://doi.org/10.4310/jsg.2019.v17.n4.a1","url":null,"abstract":"We show that simply connected contact manifolds that are subcritically Stein fillable have a unique symplectically aspherical filling up to diffeomorphism. Various extensions to manifolds with non-trivial fundamental group are discussed. The proof rests on homological restrictions on symplectic fillings derived from a degree-theoretic analysis of the evaluation map on a suitable moduli space of holomorphic spheres. Applications of this homological result include a proof that compositions of right-handed Dehn twists on Liouville domains are of infinite order in the symplectomorphism group. We also derive uniqueness results for subcritical Stein fillings up to homotopy equivalence and, under some topological assumptions on the contact manifold, up to diffeomorphism or symplectomorphism.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"3 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2016-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87227664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 44
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