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SYZ Mirrors in non-Abelian 3d Mirror Symmetry 非阿贝尔三维镜像对称中的 SYZ 镜像
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-18 DOI: arxiv-2408.09479
Ki Fung Chan, Naichung Conan Leung
{"title":"SYZ Mirrors in non-Abelian 3d Mirror Symmetry","authors":"Ki Fung Chan, Naichung Conan Leung","doi":"arxiv-2408.09479","DOIUrl":"https://doi.org/arxiv-2408.09479","url":null,"abstract":"In the SYZ program, the mirror of (Y) is the moduli space of Lagrangian\u0000branes in (Y). When (Y) is equipped with a Hamiltonian (G)-action, we\u0000prove that its mirror determines a canonical complex Lagrangian subvariety in\u0000the Coulomb branch of the 3d (mathcal{N}=4) pure (G)-gauge theory.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An $L_infty$ structure on symplectic cohomology 交映同调上的 $L_infty$ 结构
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-17 DOI: arxiv-2408.09163
Matthew Strom Borman, Mohamed El Alami, Nick Sheridan
{"title":"An $L_infty$ structure on symplectic cohomology","authors":"Matthew Strom Borman, Mohamed El Alami, Nick Sheridan","doi":"arxiv-2408.09163","DOIUrl":"https://doi.org/arxiv-2408.09163","url":null,"abstract":"We construct the $L_infty$ structure on symplectic cohomology of a Liouville\u0000domain, together with an enhancement of the closed--open map to an $L_infty$\u0000homomorphism from symplectic cochains to Hochschild cochains on the wrapped\u0000Fukaya category. Features of our construction are that it respects a modified\u0000action filtration (in contrast to Pomerleano--Seidel's construction); it uses a\u0000compact telescope model (in contrast to Abouzaid--Groman--Varolgunes'\u0000construction); and it is adapted to the purposes of our follow-up work where we\u0000construct Maurer--Cartan elements in symplectic cochains which are associated\u0000to a normal-crossings compactification of the Liouville domain.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symplectic rational homology ball fillings of Seifert fibered spaces 塞弗特纤维空间的交映理性同调球填充
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-17 DOI: arxiv-2408.09292
John B. Etnyre, Burak Ozbagci, Bülent Tosun
{"title":"Symplectic rational homology ball fillings of Seifert fibered spaces","authors":"John B. Etnyre, Burak Ozbagci, Bülent Tosun","doi":"arxiv-2408.09292","DOIUrl":"https://doi.org/arxiv-2408.09292","url":null,"abstract":"We characterize when some small Seifert fibered spaces can be the convex\u0000boundary of a symplectic rational homology ball and give strong restrictions\u0000for others to bound such manifolds. As part of this, we show that the only\u0000spherical $3$-manifolds that are the boundary of a symplectic rational homology\u0000ball are the lens spaces $L(p^2,pq-1)$ found by Lisca and give evidence for the\u0000Gompf conjecture that Brieskorn spheres do not bound Stein domains in C^2. We\u0000also find restrictions on Lagrangian disk fillings of some Legendrian knots in\u0000small Seifert fibered spaces.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Maurer--Cartan elements in symplectic cohomology from compactifications 毛雷尔--来自压实的交映同调中的卡尔坦元素
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-17 DOI: arxiv-2408.09221
Matthew Strom Borman, Mohamed El Alami, Nick Sheridan
{"title":"Maurer--Cartan elements in symplectic cohomology from compactifications","authors":"Matthew Strom Borman, Mohamed El Alami, Nick Sheridan","doi":"arxiv-2408.09221","DOIUrl":"https://doi.org/arxiv-2408.09221","url":null,"abstract":"We prove that under certain conditions, a normal crossings compactification\u0000of a Liouville domain determines a Maurer--Cartan element for the $L_infty$\u0000structure on its symplectic cohomology; and deforming by this element gives the\u0000quantum cohomology of the compactification.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202102","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization 通过对称性实现球面上面积保全映射的霍弗增长二分法
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-16 DOI: arxiv-2408.08854
Lev Buhovsky, Ben Feuerstein, Leonid Polterovich, Egor Shelukhin
{"title":"A dichotomy for the Hofer growth of area preserving maps on the sphere via symmetrization","authors":"Lev Buhovsky, Ben Feuerstein, Leonid Polterovich, Egor Shelukhin","doi":"arxiv-2408.08854","DOIUrl":"https://doi.org/arxiv-2408.08854","url":null,"abstract":"We prove that autonomous Hamiltonian flows on the two-sphere exhibit the\u0000following dichotomy: the Hofer norm either grows linearly or is bounded in time\u0000by a universal constant C. Our approach involves a new technique, Hamiltonian\u0000symmetrization. Essentially, we prove that every autonomous Hamiltonian\u0000diffeomorphism is conjugate to an element C-close in the Hofer metric to one\u0000generated by a function of the height.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Symplectic cohomology relative to a smooth anticanonical divisor 相对于光滑反偶函数除数的交映同调
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-16 DOI: arxiv-2408.09039
Daniel Pomerleano, Paul Seidel
{"title":"Symplectic cohomology relative to a smooth anticanonical divisor","authors":"Daniel Pomerleano, Paul Seidel","doi":"arxiv-2408.09039","DOIUrl":"https://doi.org/arxiv-2408.09039","url":null,"abstract":"For a monotone symplectic manifold and a smooth anticanonical divisor, there\u0000is a formal deformation of the symplectic cohomology of the divisor complement,\u0000defined by allowing Floer cylinders to intersect the divisor. We compute this\u0000deformed symplectic cohomology, in terms of the ordinary cohomology of the\u0000manifold and divisor; and also describe some additional structures that it\u0000carries.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202104","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the Algebra of the Infrared with Twisted Masses 论具有扭曲质量的红外线代数
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-15 DOI: arxiv-2408.08372
Ahsan Z. Khan, Gregory W. Moore
{"title":"On the Algebra of the Infrared with Twisted Masses","authors":"Ahsan Z. Khan, Gregory W. Moore","doi":"arxiv-2408.08372","DOIUrl":"https://doi.org/arxiv-2408.08372","url":null,"abstract":"The Algebra of the Infrared cite{Gaiotto:2015aoa} is a framework to\u0000construct local observables, interfaces, and categories of supersymmetric\u0000boundary conditions of massive $mathcal{N}=(2,2)$ theories in two dimensions\u0000by using information only about the BPS sector. The resulting framework is\u0000known as the ``web-based formalism.'' In this paper we initiate the\u0000generalization of the web-based formalism to include a much wider class of\u0000$mathcal{N}=(2,2)$ quantum field theories than was discussed in\u0000cite{Gaiotto:2015aoa}: theories with non-trivial twisted masses. The essential\u0000new ingredient is the presence of BPS particles within a fixed vacuum sector.\u0000In this paper we work out the web-based formalism for the simplest class of\u0000theories that allow for such BPS particles: theories with a single vacuum and a\u0000single twisted mass. We show that even in this simple setting there are\u0000interesting new phenomenon including the emergence of Fock spaces of closed\u0000solitons and a natural appearance of Koszul dual algebras. Mathematically,\u0000studying theories with twisted masses includes studying the Fukaya-Seidel\u0000category of A-type boundary conditions for Landau-Ginzburg models defined by a\u0000closed holomorphic one-form. This paper sketches a web-based construction for\u0000the category of A-type boundary conditions for one-forms with a single Morse\u0000zero and a single non-trivial period. We demonstrate our formalism explicitly\u0000in a particularly instructive example.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202241","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the projection of exact Lagrangians in locally conformally symplectic geometry 论局部共形对称几何中精确拉格朗日的投影
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-14 DOI: arxiv-2408.07760
Adrien Currier
{"title":"On the projection of exact Lagrangians in locally conformally symplectic geometry","authors":"Adrien Currier","doi":"arxiv-2408.07760","DOIUrl":"https://doi.org/arxiv-2408.07760","url":null,"abstract":"In this paper, we construct examples of exact Lagrangians (of \"locally\u0000conformally symplectic\" type) in cotangent bundles of closed manifolds with\u0000locally conformally symplectic structures and give conditions under which the\u0000projection induces a simple homotopy equivalence between an exact Lagrangian\u0000and the $0$-section of the cotangent bundle. This line of questioning follows\u0000in the footsteps of Abouzaid and Kragh, and more generally of the Arnol'd\u0000conjecture. Notably, we will see that while exact Lagrangians cannot be spheres\u0000in this setting, a naive adaptation of the Abouzaid-Kragh theorem does not hold\u0000in this generalization.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202107","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The spectral diameter of a symplectic ellipsoid 交映椭圆体的光谱直径
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-13 DOI: arxiv-2408.07214
Habib Alizadeh, Marcelo S. Atallah, Dylan Cant
{"title":"The spectral diameter of a symplectic ellipsoid","authors":"Habib Alizadeh, Marcelo S. Atallah, Dylan Cant","doi":"arxiv-2408.07214","DOIUrl":"https://doi.org/arxiv-2408.07214","url":null,"abstract":"The spectral diameter of a symplectic ball is shown to be equal to its\u0000capacity; this result upgrades the known bound by a factor of two and yields a\u0000simple formula for the spectral diameter of a symplectic ellipsoid. We also\u0000study the relationship between the spectral diameter and packings by two balls.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202209","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A Relative Poincaré-Birkhoff theorem 相对波恩卡-伯克霍夫定理
arXiv - MATH - Symplectic Geometry Pub Date : 2024-08-13 DOI: arxiv-2408.06919
Agustin Moreno, Arthur Limoge
{"title":"A Relative Poincaré-Birkhoff theorem","authors":"Agustin Moreno, Arthur Limoge","doi":"arxiv-2408.06919","DOIUrl":"https://doi.org/arxiv-2408.06919","url":null,"abstract":"In arXiv:2011.06562, the first author and Otto van Koert proved a generalized\u0000version of the classical Poincar'e-Birkhoff theorem, for Liouville domains of\u0000any dimension. In this article, we prove a relative version for Lagrangians\u0000with Legendrian boundary. This gives interior chords of arbitrary large length,\u0000provided the twist condition introduced in arXiv:2011.06562 is satisfied. The\u0000motivation comes from finding spatial consecutive collision orbits of arbitrary\u0000large length in the spatial circular restricted three-body problem, which are\u0000relevant for gravitational assist in the context of orbital mechanics. This is\u0000an application of a local version of wrapped Floer homology, which we introduce\u0000as the open string analogue of local Floer homology for closed strings.","PeriodicalId":501155,"journal":{"name":"arXiv - MATH - Symplectic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142202108","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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