发布求助
文献互助 智能选刊 最新文献

Journal of Symplectic Geometry最新文献

筛选
英文 中文
Poisson maps between character varieties: gluing and capping 性状品种间的泊松图:胶合和封盖
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2021-04-12 DOI: 10.4310/JSG.2022.v20.n6.a2
I. Biswas, J. Hurtubise, L. Jeffrey, Sean Lawton
{"title":"Poisson maps between character varieties: gluing and capping","authors":"I. Biswas, J. Hurtubise, L. Jeffrey, Sean Lawton","doi":"10.4310/JSG.2022.v20.n6.a2","DOIUrl":"https://doi.org/10.4310/JSG.2022.v20.n6.a2","url":null,"abstract":"Let G be a compact Lie group or a complex reductive affine algebraic group. We explore induced mappings between G-character varieties of surface groups by mappings between corresponding surfaces. It is shown that these mappings are generally Poisson. We also given an effective algorithm to compute the Poisson bi-vectors when G=SL(2,C). We demonstrate this algorithm by explicitly calculating the Poisson bi-vector for the 5-holed sphere, the first example for an Euler characteristic -3 surface.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81974045","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
A max inequality for spectral invariants of disjointly supported Hamiltonians 非联合支持哈密顿量谱不变量的一个极大不等式
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2021-02-15 DOI: 10.4310/jsg.2022.v20.n5.a6
Shira Tanny
{"title":"A max inequality for spectral invariants of disjointly supported Hamiltonians","authors":"Shira Tanny","doi":"10.4310/jsg.2022.v20.n5.a6","DOIUrl":"https://doi.org/10.4310/jsg.2022.v20.n5.a6","url":null,"abstract":"We study the relation between spectral invariants of disjointly supported Hamiltonians and of their sum. On aspherical manifolds, such a relation was established by Humili`ere, Le Roux and Seyfaddini. We show that a weaker statement holds in a wider setting, and derive applications to Polterovich's Poisson bracket invariant and to Entov and Polterovich's notion of superheavy sets.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86228840","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
Chekanov-Eliashberg $mathrm{dg}$-algebras for singular Legendrians 奇异Legendrians的Chekanov-Eliashberg $ mathm {dg}$-代数
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2021-02-09 DOI: 10.4310/JSG.2022.v20.n3.a1
J. Asplund, T. Ekholm
{"title":"Chekanov-Eliashberg $mathrm{dg}$-algebras for singular Legendrians","authors":"J. Asplund, T. Ekholm","doi":"10.4310/JSG.2022.v20.n3.a1","DOIUrl":"https://doi.org/10.4310/JSG.2022.v20.n3.a1","url":null,"abstract":"The Chekanov-Eliashberg dg-algebra is a holomorphic curve invariant associated to Legendrian submanifolds of a contact manifold. We extend the definition to Legendrian embeddings of skeleta of Weinstein manifolds. Via Legendrian surgery, the new definition gives direct proofs of wrapped Floer cohomology push-out diagrams. It also leads to a proof of a conjectured isomorphism between partially wrapped Floer cohomology and Chekanov-Eliashberg dg-algebras with coefficients in chains on the based loop space.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78793774","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
Geometric quantization of $b$-symplectic manifolds b -辛流形的几何量化
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2021-01-01 DOI: 10.4310/JSG.2021.V19.N1.A1
M. Braverman, Yiannis Loizides, Yanli Song
{"title":"Geometric quantization of $b$-symplectic manifolds","authors":"M. Braverman, Yiannis Loizides, Yanli Song","doi":"10.4310/JSG.2021.V19.N1.A1","DOIUrl":"https://doi.org/10.4310/JSG.2021.V19.N1.A1","url":null,"abstract":"We introduce a method of geometric quantization for compact $b$-symplectic manifolds in terms of the index of an Atiyah-Patodi-Singer (APS) boundary value problem. We show further that b-symplectic manifolds have canonical Spin-c structures in the usual sense, and that the APS index above coincides with the index of the Spin-c Dirac operator. We show that if the manifold is endowed with a Hamiltonian action of a compact connected Lie group with non-zero modular weights, then this method satisfies the Guillemin-Sternberg ``quantization commutes with reduction'' property. In particular our quantization coincides with the formal quantization defined by Guillemin, Miranda and Weitsman, providing a positive answer to a question posed in their paper.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79026355","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
Asymptotic behavior of exotic Lagrangian tori $T_{a,b,c}$ in $mathbb{C}P^2$ as $a+b+c to infty$ $mathbb{C}P^2$ as中奇异拉格朗日环面$T_{a,b,c}$的渐近行为 $a+b+c to infty$
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2021-01-01 DOI: 10.4310/jsg.2021.v19.n3.a4
Weonmo Lee, Y. Oh, Renato Vianna
{"title":"Asymptotic behavior of exotic Lagrangian tori $T_{a,b,c}$ in $mathbb{C}P^2$ as $a+b+c to infty$","authors":"Weonmo Lee, Y. Oh, Renato Vianna","doi":"10.4310/jsg.2021.v19.n3.a4","DOIUrl":"https://doi.org/10.4310/jsg.2021.v19.n3.a4","url":null,"abstract":"","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83358165","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
Genus-one complex quantum Chern–Simons theory 第一类复量子陈-西蒙斯理论
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2020-12-31 DOI: 10.4310/JSG.2022.v20.n6.a1
J. Andersen, A. Malusà, Gabriele Rembado
{"title":"Genus-one complex quantum Chern–Simons theory","authors":"J. Andersen, A. Malusà, Gabriele Rembado","doi":"10.4310/JSG.2022.v20.n6.a1","DOIUrl":"https://doi.org/10.4310/JSG.2022.v20.n6.a1","url":null,"abstract":"We consider the geometric quantisation of Chern--Simons theory for closed genus-one surfaces and semisimple complex groups. First we introduce the natural complexified analogue of the Hitchin connection in K\"{a}hler quantisation, with polarisations coming from the nonabelian Hodge hyper-K\"{a}hler geometry of the moduli spaces of flat connections, thereby complementing the real-polarised approach of Witten. Then we consider the connection of Witten, and we identify it with the complexified Hitchin connection using a version of the Bargmann transform on polarised sections over the moduli spaces.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87941127","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
Polyhedral approximation by Lagrangian and isotropic tori 拉格朗日和各向同性环面的多面体逼近
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2020-12-10 DOI: 10.4310/jsg.2022.v20.n6.a4
Yann Rollin
{"title":"Polyhedral approximation by Lagrangian and isotropic tori","authors":"Yann Rollin","doi":"10.4310/jsg.2022.v20.n6.a4","DOIUrl":"https://doi.org/10.4310/jsg.2022.v20.n6.a4","url":null,"abstract":"We prove that every smoothly immersed 2-torus of $mathbb{R}^4$ can be approximated, in the C0-sense, by immersed polyhedral Lagrangian tori. In the case of a smoothly immersed (resp. embedded) Lagrangian torus of $mathbb{R}^4$, the surface can be approximated in the C1-sense by immersed (resp. embedded) polyhedral Lagrangian tori. Similar statements are proved for isotropic 2-tori of $mathbb{R}^{2n}$.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78106769","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: 1
Reductive subalgebras of semisimple Lie algebras and Poisson commutativity 半单李代数的约化子代数与泊松交换性
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2020-12-07 DOI: 10.4310/jsg.2022.v20.n4.a4
D. Panyushev, O. Yakimova
{"title":"Reductive subalgebras of semisimple Lie algebras and Poisson commutativity","authors":"D. Panyushev, O. Yakimova","doi":"10.4310/jsg.2022.v20.n4.a4","DOIUrl":"https://doi.org/10.4310/jsg.2022.v20.n4.a4","url":null,"abstract":"Let $mathfrak g$ be a semisimple Lie algebra, $mathfrak hsubsetmathfrak g$ a reductive subalgebra such that $mathfrak h^perp$ is a complementary $mathfrak h$-submodule of $mathfrak g$. In 1983, Bogoyavlenski claimed that one obtains a Poisson commutative subalgebra of the symmetric algebra ${mathcal S}(mathfrak g)$ by taking the subalgebra ${mathcal Z}$ generated by the bi-homogeneous components of all $Hin{mathcal S}(mathfrak g)^{mathfrak g}$. But this is false, and we present a counterexample. We also provide a criterion for the Poisson commutativity of such subalgebras ${mathcal Z}$. As a by-product, we prove that ${mathcal Z}$ is Poisson commutative if $mathfrak h$ is abelian and describe ${mathcal Z}$ in the special case when $mathfrak h$ is a Cartan subalgebra. In this case, ${mathcal Z}$ appears to be polynomial and has the maximal transcendence degree $(mathrm{dim},mathfrak g+mathrm{rk},mathfrak g)/2$.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72588245","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: 1
On the minimal symplectic area of Lagrangians 关于拉格朗日算子的最小辛面积
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2020-12-05 DOI: 10.4310/jsg.2022.v20.n6.a5
Zhengyi Zhou
{"title":"On the minimal symplectic area of Lagrangians","authors":"Zhengyi Zhou","doi":"10.4310/jsg.2022.v20.n6.a5","DOIUrl":"https://doi.org/10.4310/jsg.2022.v20.n6.a5","url":null,"abstract":"We show that the minimal symplectic area of Lagrangian submanifolds are universally bounded in symplectically aspherical domains with vanishing symplectic cohomology. If an exact domain admits a $k$-semi-dilation, then the minimal symplectic area is universally bounded for $K(pi,1)$-Lagrangians. As a corollary, we show that Arnold chord conjecture holds for the following four cases: (1) $Y$ admits an exact filling with $SH^*(W)=0$ (for some ring coefficient); (2) $Y$ admits a symplectically aspherical filling with $SH^*(W)=0$ and simply connected Legendrians; (3) $Y$ admits an exact filling with a $k$-semi-dilation and the Legendrian is a $K(pi,1)$ space; (4) $Y$ is the cosphere bundle $S^*Q$ with $pi_2(Q)to H_2(Q)$ nontrivial and the Legendrian has trivial $pi_2$. In addition, we obtain the existence of homoclinic orbits in case (1). We also provide many more examples with $k$-semi-dilations in all dimensions $ge 4$.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78600464","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
Real and complex hedgehogs, their symplectic area, curvature and evolutes 真实的和复杂的刺猬，它们的辛面积，曲率和进化
IF 0.7 3区 数学
Journal of Symplectic Geometry Pub Date : 2020-09-24 DOI: 10.4310/jsg.2021.v19.n3.a3
Yves Martinez-Maure
{"title":"Real and complex hedgehogs, their symplectic area, curvature and evolutes","authors":"Yves Martinez-Maure","doi":"10.4310/jsg.2021.v19.n3.a3","DOIUrl":"https://doi.org/10.4310/jsg.2021.v19.n3.a3","url":null,"abstract":"Classical (real) hedgehogs can be regarded as the geometrical realiza-tions of formal di¤erences of convex bodies in R n+1. Like convex bodies, hedgehogs can be identi…ed with their support functions. Adopting a pro-jective viewpoint, we prove that any holomorphic function h : C n ! C can be regarded as the 'support function' of a complex hedgehog H h in C n+1. In the same vein, we introduce the notion of evolute of such a hedgehog H h in C 2 , and a natural (but apparently hitherto unknown) notion of complex curvature, which allows us to interpret this evolute as the locus of the centers of complex curvature. It is of course permissible to think that the development of a 'Brunn-Minkowski theory for complex hedgehogs' (replacing Euclidean volumes by symplectic ones) might be a promising way of research. We give …rst two results in this direction. We next return to real hedgehogs in R 2n endowed with a linear complex structure. We introduce and study the notion of evolute of a hedgehog. We particularly focus our attention on R 4 endowed with a linear Kahler structure determined by the datum of a pure unit quaternion. In parallel, we study the symplectic area of the images of the oriented Hopf circles under hedgehog parametrizations and introduce a quaternionic curvature function for such an image. Finally, we consider brie ‡y the convolution of hedgehogs, and the particular case of hedgehogs in R 4n regarded as a hyperkahler vector space.","PeriodicalId":50029,"journal":{"name":"Journal of Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.7,"publicationDate":"2020-09-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87191255","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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信