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Moser–Greene–Shiohama stability for families 家庭的moser - green - shiohama稳定性
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2019-01-01 DOI: 10.4310/jsg.2019.v17.n5.a6
Á. Pelayo, Xiudi Tang
{"title":"Moser–Greene–Shiohama stability for families","authors":"Á. Pelayo, Xiudi Tang","doi":"10.4310/jsg.2019.v17.n5.a6","DOIUrl":"https://doi.org/10.4310/jsg.2019.v17.n5.a6","url":null,"abstract":"Let M be a noncompact oriented connected manifold and let B be a compact manifold. We give conditions on two smooth families of volume forms { ω p } p ∈ B , { τ p } p ∈ B which guarantee the existence of a smooth family of diffeomorphisms { ϕ p } p ∈ B such that ϕ ∗ p ω p = τ p for all p ∈ B . If B is a point, our result recovers a theorem of Greene and Shiohama from 1979, which itself extended a theorem of Moser for compact manifolds.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"13 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73208579","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
Contact surgeries on Legendrian figure-eight knots 联系勒让德式八字结手术
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2019-01-01 DOI: 10.4310/jsg.2019.v17.n4.a4
J. Conway
{"title":"Contact surgeries on Legendrian figure-eight knots","authors":"J. Conway","doi":"10.4310/jsg.2019.v17.n4.a4","DOIUrl":"https://doi.org/10.4310/jsg.2019.v17.n4.a4","url":null,"abstract":"We show that all positive contact surgeries on every Legendrian figure-eight knot in ( S 3 , ξ std ) result in an overtwisted contact structure. The proof uses convex surface theory and invariants from Heegaard Floer homology.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"10 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88922512","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
Interface asymptotics of partial Bergman kernels on $S^1$-symmetric Kähler manifolds S^1$-对称Kähler流形上部分Bergman核的界面渐近性
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2019-01-01 DOI: 10.4310/jsg.2019.v17.n3.a6
S. Zelditch, Peng Zhou
{"title":"Interface asymptotics of partial Bergman kernels on $S^1$-symmetric Kähler manifolds","authors":"S. Zelditch, Peng Zhou","doi":"10.4310/jsg.2019.v17.n3.a6","DOIUrl":"https://doi.org/10.4310/jsg.2019.v17.n3.a6","url":null,"abstract":"","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"1 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89141503","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: 22
A characterisation of toric locally conformally Kähler manifolds 环面局部共形Kähler流形的表征
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2019-01-01 DOI: 10.4310/jsg.2019.v17.n5.a2
Nicolina Istrati
{"title":"A characterisation of toric locally conformally Kähler manifolds","authors":"Nicolina Istrati","doi":"10.4310/jsg.2019.v17.n5.a2","DOIUrl":"https://doi.org/10.4310/jsg.2019.v17.n5.a2","url":null,"abstract":"We prove that a compact toric locally conformally K¨ahler manifold which is not K¨ahler admits a toric Vaisman structure. This is the final step leading to the classification of compact toric locally conformally K¨ahler manifolds. We also show, by constructing an example, that unlike in the symplectic case, toric locally conformally symplectic manifolds are not necessarily toric locally conformally K¨ahler.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"73 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81757668","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
Superheavy Lagrangian immersions in surfaces 表面的超重拉格朗日浸入
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2019-01-01 DOI: 10.4310/JSG.2019.V17.N1.A5
Morimichi Kawasaki
{"title":"Superheavy Lagrangian immersions in surfaces","authors":"Morimichi Kawasaki","doi":"10.4310/JSG.2019.V17.N1.A5","DOIUrl":"https://doi.org/10.4310/JSG.2019.V17.N1.A5","url":null,"abstract":"We show that the union of some circles in a closed Riemannian surface with positive genus is superheavy in the sense of Entov-Polterovich. By a result of Entov and Polterovich, this implies that the product of this union and the Clifford torus of C P n with the Fubini-Study symplectic form cannot be displaced by any symplec-tomorphisms.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"41 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88230654","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
Futaki invariant for Fedosov star products 费多索夫星积的Futaki不变量
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2019-01-01 DOI: 10.4310/jsg.2019.v17.n5.a3
Laurent La Fuente-Gravy
{"title":"Futaki invariant for Fedosov star products","authors":"Laurent La Fuente-Gravy","doi":"10.4310/jsg.2019.v17.n5.a3","DOIUrl":"https://doi.org/10.4310/jsg.2019.v17.n5.a3","url":null,"abstract":"We study obstructions to the existence of closed Fedosov star products on a given Kähler manifold (M,ω, J). In our previous paper [14], we proved that the Levi-Civita connection of a Kähler manifold will produce a closed Fedosov star product (closed in the sense of Connes–Flato–Sternheimer [4]) only if it is a zero of a moment map μ on the space of symplectic connections. By analogy with the Futaki invariant obstructing the existence of constant scalar curvature Kähler metric, we build an obstruction for the existence of zero of μ and hence for the existence of closed Fedosov star product on a Kähler manifold.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"43 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81660291","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
$mathrm{QP}$-structures of degree $3$ and $mathsf{CLWX} : 2$-algebroids $mathsf{QP}$- 3次代数元和$mathsf{CLWX} : 2次代数元的结构
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2019-01-01 DOI: 10.4310/jsg.2019.v17.n6.a8
Jiefeng Liu, Y. Sheng
{"title":"$mathrm{QP}$-structures of degree $3$ and $mathsf{CLWX} : 2$-algebroids","authors":"Jiefeng Liu, Y. Sheng","doi":"10.4310/jsg.2019.v17.n6.a8","DOIUrl":"https://doi.org/10.4310/jsg.2019.v17.n6.a8","url":null,"abstract":"","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"82 5 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89586791","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
Equidistributed periodic orbits of $C^infty$-generic three-dimensional Reeb flows $C^infty$的等分布周期轨道-一般三维Reeb流
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-12-05 DOI: 10.4310/jsg.2021.v19.n3.a2
Kei Irie
{"title":"Equidistributed periodic orbits of $C^infty$-generic three-dimensional Reeb flows","authors":"Kei Irie","doi":"10.4310/jsg.2021.v19.n3.a2","DOIUrl":"https://doi.org/10.4310/jsg.2021.v19.n3.a2","url":null,"abstract":"We prove that, for a $C^infty$-generic contact form $lambda$ adapted to a given contact distribution on a closed three-manifold, there exists a sequence of periodic Reeb orbits which is equidistributed with respect to $dlambda$. This is a quantitative refinement of the $C^infty$-generic density theorem for three-dimensional Reeb flows, which was previously proved by the author. The proof is based on the volume theorem in embedded contact homology (ECH) by Cristofaro-Gardiner, Hutchings, Ramos, and inspired by the argument of Marques-Neves-Song, who proved a similar equidistribution result for minimal hypersurfaces. We also discuss a question about generic behavior of periodic Reeb orbits \"representing\" ECH homology classes, and give a partial affirmative answer to a toy model version of this question which concerns boundaries of star-shaped toric domains.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"15 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72835663","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
An unoriented skein relation via bordered–sutured Floer homology 通过有边缝合花同源的无取向绞结关系
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-10-31 DOI: 10.4310/jsg.2021.v19.n6.a4
D. Vela-Vick, C.-M. Michael Wong
{"title":"An unoriented skein relation via bordered–sutured Floer homology","authors":"D. Vela-Vick, C.-M. Michael Wong","doi":"10.4310/jsg.2021.v19.n6.a4","DOIUrl":"https://doi.org/10.4310/jsg.2021.v19.n6.a4","url":null,"abstract":"We show that the bordered-sutured Floer invariant of the complement of a tangle in an arbitrary 3-manifold $Y$, with minimal conditions on the bordered-sutured structure, satisfies an unoriented skein exact triangle. This generalizes a theorem by Manolescu for links in $S^3$. We give a theoretical proof of this result by adapting holomorphic polygon counts to the bordered-sutured setting, and also give a combinatorial description of all maps involved and explicitly compute them. We then show that, for $Y = S^3$, our exact triangle coincides with Manolescu's. Finally, we provide a graded version of our result, explaining in detail the grading reduction process involved.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"113 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79600160","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
H-principle for complex contact structures on Stein manifolds Stein流形上复杂接触结构的h原理
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2018-10-30 DOI: 10.4310/JSG.2020.V18.N3.A4
F. Forstnerič
{"title":"H-principle for complex contact structures on Stein manifolds","authors":"F. Forstnerič","doi":"10.4310/JSG.2020.V18.N3.A4","DOIUrl":"https://doi.org/10.4310/JSG.2020.V18.N3.A4","url":null,"abstract":"In this paper we introduce the notion of a formal complex contact structure on an odd dimensional complex manifold. Our main result is that every formal complex contact structure on a Stein manifold $X$ is homotopic to a holomorphic contact structure on a Stein domain $Omegasubset X$ which is diffeotopic to $X$. We also prove a parametric h-principle in this setting, analogous to Gromov's h-principle for contact structures on smooth open manifolds. On Stein threefolds we obtain a complete homotopy classification of formal complex contact structures. Our methods also furnish a parametric h-principle for germs of holomorphic contact structures along totally real submanifolds of class $mathscr C^2$ in arbitrary complex manifolds.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":"73 1","pages":""},"PeriodicalIF":0.7,"publicationDate":"2018-10-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86163781","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
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