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Journal of Symplectic Geometry最新文献

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Epsilon-non-squeezing and $C^0$-rigidity of epsilon-symplectic embeddings 辛嵌入的非挤压和C^0$刚性
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-05-03 DOI: 10.4310/jsg.2022.v20.n5.a5
S. Muller
{"title":"Epsilon-non-squeezing and $C^0$-rigidity of epsilon-symplectic embeddings","authors":"S. Muller","doi":"10.4310/jsg.2022.v20.n5.a5","DOIUrl":"https://doi.org/10.4310/jsg.2022.v20.n5.a5","url":null,"abstract":"An embedding $varphi colon (M_1, omega_1) to (M_2, omega_2)$ (of symplectic manifolds of the same dimension) is called $epsilon$-symplectic if the difference $varphi^* omega_2 - omega_1$ is $epsilon$-small with respect to a fixed Riemannian metric on $M_1$. We prove that if a sequence of $epsilon$-symplectic embeddings converges uniformly (on compact subsets) to another embedding, then the limit is $E$-symplectic, where the number $E$ depends only on $epsilon$ and $E (epsilon) to 0$ as $epsilon to 0$. This generalizes $C^0$-rigidity of symplectic embeddings, and answers a question in topological quantum computing by Michael Freedman. As in the symplectic case, this rigidity theorem can be deduced from the existence and properties of symplectic capacities. An $epsilon$-symplectic embedding preserves capacity up to an $epsilon$-small error, and linear $epsilon$-symplectic maps can be characterized by the property that they preserve the symplectic spectrum of ellipsoids (centered at the origin) up to an error that is $epsilon$-small. We sketch an alternative proof using the shape invariant, which gives rise to an analogous characterization and rigidity theorem for $epsilon$-contact embeddings.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"30 2 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77865947","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: 3
Simple sheaves for knot conormals 简单的绳结共线
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-05-02 DOI: 10.4310/jsg.2020.v18.n4.a3
Honghao Gao
{"title":"Simple sheaves for knot conormals","authors":"Honghao Gao","doi":"10.4310/jsg.2020.v18.n4.a3","DOIUrl":"https://doi.org/10.4310/jsg.2020.v18.n4.a3","url":null,"abstract":"We classify the simple sheaves microsupported along the conormal bundle of a knot. We also establish a correspondence between simple sheaves up to local systems and augmentations, explaining the underlying reason why knot contact homology representations detect augmentations.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"333 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-05-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86785102","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: 7
Quantization of Hamiltonian coactions via twist 通过扭转的哈密顿作用的量子化
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-04-17 DOI: 10.4310/JSG.2020.V18.N2.A2
P. Bieliavsky, C. Esposito, R. Nest
{"title":"Quantization of Hamiltonian coactions via twist","authors":"P. Bieliavsky, C. Esposito, R. Nest","doi":"10.4310/JSG.2020.V18.N2.A2","DOIUrl":"https://doi.org/10.4310/JSG.2020.V18.N2.A2","url":null,"abstract":"In this paper we introduce a notion of quantum Hamiltonian (co)action of Hopf algebras endowed with Drinfel'd twist structure (resp., 2-cocycles). First, we define a classical Hamiltonian action in the setting of Poisson Lie groups compatible with the 2-cocycle stucture and we discuss a concrete example. This allows us to construct, out of the classical momentum map, a quantum momentum map in the setting of Hopf coactions and to quantize it by using Drinfel'd approach.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"14 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-04-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87624886","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
Holomorphic disks and the disk potential for a fibered Lagrangian 全纯盘和纤维拉格朗日的盘势
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-04-11 DOI: 10.4310/JSG.2021.v19.n1.a4
Douglas Schultz
{"title":"Holomorphic disks and the disk potential for a fibered Lagrangian","authors":"Douglas Schultz","doi":"10.4310/JSG.2021.v19.n1.a4","DOIUrl":"https://doi.org/10.4310/JSG.2021.v19.n1.a4","url":null,"abstract":"We consider a fibered Lagrangian $L$ in a compact symplectic fibration with small monotone fibers, and develop a strategy for lifting $J$-holomorphic disks with Lagrangian boundary from the base to the total space. In case $L$ is a product, we use this machinery to give a formula for the leading order potential and formulate an unobstructedness criteria for the $A_infty$ algebra. We provide some explicit computations, one of which involves finding an embedded 2n+k dimensional submanifold of Floer-non-trivial tori in an 2n+2k dimensional fiber bundle.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"150 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-04-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78581615","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
Bohr–Sommerfeld Lagrangian submanifolds as minima of convex functions 作为凸函数极小值的玻尔-索默菲尔德拉格朗日子流形
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-03-19 DOI: 10.4310/jsg.2020.v18.n1.a9
Alexandre Vérine
{"title":"Bohr–Sommerfeld Lagrangian submanifolds as minima of convex functions","authors":"Alexandre Vérine","doi":"10.4310/jsg.2020.v18.n1.a9","DOIUrl":"https://doi.org/10.4310/jsg.2020.v18.n1.a9","url":null,"abstract":"We prove that every closed Bohr-Sommerfeld Lagrangian submanifold $Q$ of a symplectic/K\"ahler manifold $X$ can be realised as a Morse-Bott minimum for some 'convex' exhausting function defined in the complement of a symplectic/complex hyperplane section $Y$. In the K\"ahler case, 'convex' means strictly plurisubharmonic while, in the symplectic case, it refers to the existence of a Liouville pseudogradient. In particular, $Qsubset Xsetminus Y$ is a regular Lagrangian submanifold in the sense of Eliashberg-Ganatra-Lazarev.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"18 2","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72633027","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
The shift map on Floer trajectory spaces 弗洛尔轨迹空间上的移位映射
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-03-10 DOI: 10.4310/JSG.2021.v19.n2.a2
U. Frauenfelder, Joa Weber
{"title":"The shift map on Floer trajectory spaces","authors":"U. Frauenfelder, Joa Weber","doi":"10.4310/JSG.2021.v19.n2.a2","DOIUrl":"https://doi.org/10.4310/JSG.2021.v19.n2.a2","url":null,"abstract":"In this article we give a uniform proof why the shift map on Floer homology trajectory spaces is scale smooth. This proof works for various Floer homologies, periodic, Lagrangian, Hyperk\"ahler, elliptic or parabolic, and uses Hilbert space valued Sobolev theory.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"31 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-03-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86250147","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: 7
Cahen–Gutt moment map, closed Fedosov star product and structure of the automorphism group Cahen-Gutt矩映射，闭Fedosov星积和自同构群的结构
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-02-28 DOI: 10.4310/jsg.2020.v18.n1.a3
A. Futaki, Hajime Ono
{"title":"Cahen–Gutt moment map, closed Fedosov star product and structure of the automorphism group","authors":"A. Futaki, Hajime Ono","doi":"10.4310/jsg.2020.v18.n1.a3","DOIUrl":"https://doi.org/10.4310/jsg.2020.v18.n1.a3","url":null,"abstract":"We show that if a compact Kaehler manifold $M$ admits closed Fedosov's star product then the reduced Lie algebra of holomorphic vector fields on $M$ is reductive. This comes in pair with the obstruction previously found by La Fuente-Gravy. More generally we consider the squared norm of Cahen-Gutt moment map as in the same spirit of Calabi functional for the scalar curvature in cscK problem, and prove a Cahen-Gutt version of Calabi's theorem on the structure of the Lie algebra of holomorphic vector fields for extremal Kaehler manifolds. The proof uses a Hessian formula for the squared norm of Cahen-Gutt moment map.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"82 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73448156","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: 11
Volume of small balls and sub-Riemannian curvature in 3D contact manifolds 三维接触流形中小球体积与亚黎曼曲率
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-02-27 DOI: 10.4310/jsg.2020.v18.n2.a1
D. Barilari, I. Beschastnyi, A. Lerário
{"title":"Volume of small balls and sub-Riemannian curvature in 3D contact manifolds","authors":"D. Barilari, I. Beschastnyi, A. Lerário","doi":"10.4310/jsg.2020.v18.n2.a1","DOIUrl":"https://doi.org/10.4310/jsg.2020.v18.n2.a1","url":null,"abstract":"We compute the asymptotic expansion of the volume of small sub-Riemannian balls in a contact 3-dimensional manifold, and we express the first meaningful geometric coefficients in terms of geometric invariants of the sub-Riemannian structure","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"8 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78655718","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
A compactness result for $mathcal{H}$‑holomorphic curves in symplectizations $mathcal{H}$‑全纯曲线的紧致性结果
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-02-25 DOI: 10.4310/JSG.2021.V19.N1.A2
Alexandru Doicu, Urs Fuchs
{"title":"A compactness result for $mathcal{H}$‑holomorphic curves in symplectizations","authors":"Alexandru Doicu, Urs Fuchs","doi":"10.4310/JSG.2021.V19.N1.A2","DOIUrl":"https://doi.org/10.4310/JSG.2021.V19.N1.A2","url":null,"abstract":"$mathcal{H}-$holomorphic curves are solutions of a specific modification of the pseudoholomorphic curve equation in symplectizations involving a harmonic $1-$form as perturbation term. In this paper we compactify the moduli space of $mathcal{H}-$holomorphic curves with a priori bounds on the harmonic $1-$forms.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"18 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78013029","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
Tight neighborhoods of contact submanifolds 接触子流形的紧邻域
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-02-20 DOI: 10.4310/JSG.2020.V18.N6.A4
Luis Hern'andez-Corbato, Luc'ia Mart'in-Merch'an, F. Presas
{"title":"Tight neighborhoods of contact submanifolds","authors":"Luis Hern'andez-Corbato, Luc'ia Mart'in-Merch'an, F. Presas","doi":"10.4310/JSG.2020.V18.N6.A4","DOIUrl":"https://doi.org/10.4310/JSG.2020.V18.N6.A4","url":null,"abstract":"We prove that any small enough neighborhood of a closed contact submanifold is always tight under a mild assumption on its normal bundle. The non-existence of $C^0$--small positive loops of contactomorphisms in general overtwisted manifolds is shown as a corollary.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"406 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78083372","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
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