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Symplectic geometry of electrical networks 电气网络的交映几何学
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-09-13 DOI: 10.1016/j.geomphys.2024.105323
B. Bychkov , V. Gorbounov , L. Guterman , A. Kazakov
{"title":"Symplectic geometry of electrical networks","authors":"B. Bychkov ,&nbsp;V. Gorbounov ,&nbsp;L. Guterman ,&nbsp;A. Kazakov","doi":"10.1016/j.geomphys.2024.105323","DOIUrl":"10.1016/j.geomphys.2024.105323","url":null,"abstract":"<div><div>In this paper we relate a well-known in symplectic geometry compactification of the space of symmetric bilinear forms considered as a chart of the Lagrangian Grassmannian to the specific compactifications of the space of electrical networks in the disc obtained in <span><span>[11]</span></span>, <span><span>[4]</span></span> and <span><span>[3]</span></span>. In particular, we state an explicit connection between these works and describe some of the combinatorics developed there in the language of symplectic geometry. We also show that the combinatorics of the concordance vectors forces the uniqueness of the symplectic form, such that corresponding points of the Grassmannian are isotropic. We define a notion of Lagrangian concordance which provides a construction of the compactification of the space of electrical networks in the positive part of the Lagrangian Grassmannian bypassing the construction from <span><span>[11]</span></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105323"},"PeriodicalIF":1.6,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142314212","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
Classification of irreducible conformal S(p)-modules of finite rank 有限阶不可还原共形 S(p)模块的分类
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-09-05 DOI: 10.1016/j.geomphys.2024.105312
Jianzhi Han , Yumeng Zhan
{"title":"Classification of irreducible conformal S(p)-modules of finite rank","authors":"Jianzhi Han ,&nbsp;Yumeng Zhan","doi":"10.1016/j.geomphys.2024.105312","DOIUrl":"10.1016/j.geomphys.2024.105312","url":null,"abstract":"<div><p>In the present paper, we give the classification of irreducible conformal <span><math><mi>S</mi><mo>(</mo><mi>p</mi><mo>)</mo></math></span>-modules of finite rank. This generalizes the main result in <span><span>[15]</span></span>. And in this paper we adopt a different way to obtain the classification and this method can also be used to classify finite irreducible conformal modules over many other Lie conformal superalgebras.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"206 ","pages":"Article 105312"},"PeriodicalIF":1.6,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142151434","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
Frobenius and commutative pseudomonoids in the bicategory of spans 跨度二分类中的弗罗本尼斯和交换假单子
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-09-04 DOI: 10.1016/j.geomphys.2024.105309
Ivan Contreras , Rajan Amit Mehta , Walker H. Stern
{"title":"Frobenius and commutative pseudomonoids in the bicategory of spans","authors":"Ivan Contreras ,&nbsp;Rajan Amit Mehta ,&nbsp;Walker H. Stern","doi":"10.1016/j.geomphys.2024.105309","DOIUrl":"10.1016/j.geomphys.2024.105309","url":null,"abstract":"<div><p>In previous work by the first two authors, Frobenius and commutative algebra objects in the category of spans of sets were characterized in terms of simplicial sets satisfying certain properties. In this paper, we find a similar characterization for the analogous coherent structures in the bicategory of spans of sets. We show that commutative and Frobenius pseudomonoids in Span correspond, respectively, to paracyclic sets and Γ-sets satisfying the 2-Segal conditions. These results connect closely with work of the third author on <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> algebras in ∞-categories of spans, as well as the growing body of work on higher Segal objects. Because our motivation comes from symplectic geometry and topological field theory, we emphasize the direct and computational nature of the classifications and their proofs.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"207 ","pages":"Article 105309"},"PeriodicalIF":1.6,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274626","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
Biharmonic submanifolds of the quaternionic projective space 四元投影空间的双谐波子平面
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-09-04 DOI: 10.1016/j.geomphys.2024.105310
Clebes Brandão
{"title":"Biharmonic submanifolds of the quaternionic projective space","authors":"Clebes Brandão","doi":"10.1016/j.geomphys.2024.105310","DOIUrl":"10.1016/j.geomphys.2024.105310","url":null,"abstract":"<div><p>The present paper is devoted to the study of biharmonic submanifolds in quaternionic space forms. After giving the biharmonicity conditions for submanifolds in these spaces, we study different particular cases for which we obtain curvature estimates. We study biharmonic submanifolds with parallel mean curvature and biharmonic submanifolds which are pseudo-umbilical in the quaternionic projective space. We find the relation between the bitension field of the inclusion of a submanifold in the n-dimensional quaternionic projective space and the bitension field of the inclusion of the corresponding Hopf-tube in the unit sphere of dimension 4n+3.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"206 ","pages":"Article 105310"},"PeriodicalIF":1.6,"publicationDate":"2024-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142151435","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
On Koszul complex of a supermodule 论超模的科斯祖尔复数
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-09-03 DOI: 10.1016/j.geomphys.2024.105311
Darío Sánchez Gómez, Fernando Sancho de Salas
{"title":"On Koszul complex of a supermodule","authors":"Darío Sánchez Gómez,&nbsp;Fernando Sancho de Salas","doi":"10.1016/j.geomphys.2024.105311","DOIUrl":"10.1016/j.geomphys.2024.105311","url":null,"abstract":"<div><p>This paper is devoted to an exposition of the Koszul complex of a supermodule and its Berezinian from an intrinsic and as general as possible point of view. As an application, an analogue to Bott's formula in the supercommutative setting is given, computing the cohomology of twisted differential <em>p</em>-forms on the projective superspace.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"206 ","pages":"Article 105311"},"PeriodicalIF":1.6,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0393044024002122/pdfft?md5=032fd99271ed5796fe81c1d33aee29f9&pid=1-s2.0-S0393044024002122-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142164168","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
On the existence of heterotic-string and type-II-superstring field theory vertices 论异弦和II型超弦场论顶点的存在
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-08-30 DOI: 10.1016/j.geomphys.2024.105307
Seyed Faroogh Moosavian , Yehao Zhou
{"title":"On the existence of heterotic-string and type-II-superstring field theory vertices","authors":"Seyed Faroogh Moosavian ,&nbsp;Yehao Zhou","doi":"10.1016/j.geomphys.2024.105307","DOIUrl":"10.1016/j.geomphys.2024.105307","url":null,"abstract":"<div><p>We consider the problem of the existence of heterotic-string and type-II-superstring field theory vertices in the product of spaces of bordered surfaces parameterizing the left- and right-moving sectors of these theories. It turns out that this problem can be solved by proving the existence of a solution to the BV quantum master equation in moduli spaces of bordered spin-Riemann surfaces. We first prove that for arbitrary genus <figure><img></figure>, <figure><img></figure> Neveu–Schwarz boundary components, and <figure><img></figure> Ramond boundary components such solutions exist. We also prove that these solutions are unique up to homotopy in the category of BV algebras. Furthermore, we prove that there exists a map in this category under which these solutions are mapped to fundamental classes of Deligne-Mumford stacks of associated punctured spin-Riemann surfaces. These results generalize the work of Costello on the existence of a solution to the BV quantum master equations in moduli spaces of bordered Riemann surfaces which, through the work of Sen and Zwiebach, are related to the existence of bosonic-string vertices, and their relation to fundamental classes of Deligne-Mumford stacks of associated punctured Riemann surfaces. Using the existence of solutions to the BV quantum master equation in moduli spaces of spin-Riemann surfaces, we prove that heterotic-string and type-II-superstring field theory vertices, for arbitrary genus <figure><img></figure> and an arbitrary number of any type of boundary components, exist. Furthermore, we prove the existence of a solution to the BV quantum master equation in spaces of bordered <span><math><mi>N</mi><mo>=</mo><mn>1</mn></math></span> super-Riemann surfaces for arbitrary genus <figure><img></figure>, <figure><img></figure> Neveu–Schwarz boundary components, and <figure><img></figure> Ramond boundary components.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"205 ","pages":"Article 105307"},"PeriodicalIF":1.6,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0393044024002080/pdfft?md5=505731ce4399fd155920479cebe89a0a&pid=1-s2.0-S0393044024002080-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Formal deformations, cohomology theory and L∞[1]-structures for differential Lie algebras of arbitrary weight 任意权重微分列阵的形式变形、同调理论和 L∞[1] 结构
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-08-30 DOI: 10.1016/j.geomphys.2024.105308
Weiguo Lyu , Zihao Qi , Jian Yang , Guodong Zhou
{"title":"Formal deformations, cohomology theory and L∞[1]-structures for differential Lie algebras of arbitrary weight","authors":"Weiguo Lyu ,&nbsp;Zihao Qi ,&nbsp;Jian Yang ,&nbsp;Guodong Zhou","doi":"10.1016/j.geomphys.2024.105308","DOIUrl":"10.1016/j.geomphys.2024.105308","url":null,"abstract":"<div><p>We introduced a cohomology theory for differential Lie algebras of arbitrary weight which generalised a previous work of Jiang and Sheng. The underlying <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>[</mo><mn>1</mn><mo>]</mo></math></span>-structure on the cochain complex is also determined via a generalised version of higher derived brackets. The equivalence between <span><math><msub><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msub><mo>[</mo><mn>1</mn><mo>]</mo></math></span>-structures for absolute and relative differential Lie algebras is established. Formal deformations and abelian extensions are interpreted by using lower degree cohomology groups. Also we introduce the homotopy differential Lie algebras.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"205 ","pages":"Article 105308"},"PeriodicalIF":1.6,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142158465","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
Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers 跨代数谱曲线上的拓扑递归和阿特兰迪斯-赫尔维茨数
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-08-23 DOI: 10.1016/j.geomphys.2024.105306
Vincent Bouchard , Reinier Kramer , Quinten Weller
{"title":"Topological recursion on transalgebraic spectral curves and Atlantes Hurwitz numbers","authors":"Vincent Bouchard ,&nbsp;Reinier Kramer ,&nbsp;Quinten Weller","doi":"10.1016/j.geomphys.2024.105306","DOIUrl":"10.1016/j.geomphys.2024.105306","url":null,"abstract":"<div><div>Given a spectral curve with exponential singularities (which we call a “transalgebraic spectral curve”), we extend the definition of topological recursion to include contributions from the exponential singularities in a way that is compatible with limits of sequences of spectral curves. This allows us to prove the topological recursion/quantum curve correspondence for a large class of transalgebraic spectral curves. As an application, we find that Atlantes Hurwitz numbers, which were previously thought to fall outside the scope of topological recursion, satisfy (our extended version of) topological recursion, and we construct the corresponding quantum curve directly from topological recursion.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"206 ","pages":"Article 105306"},"PeriodicalIF":1.6,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142226067","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Darboux, Moser and Weinstein theorems for prequantum systems and applications to geometric quantization 前量子系统的达尔布定理、莫泽定理和温斯坦定理及其在几何量子化中的应用
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-08-22 DOI: 10.1016/j.geomphys.2024.105298
Eva Miranda , Jonathan Weitsman
{"title":"Darboux, Moser and Weinstein theorems for prequantum systems and applications to geometric quantization","authors":"Eva Miranda ,&nbsp;Jonathan Weitsman","doi":"10.1016/j.geomphys.2024.105298","DOIUrl":"10.1016/j.geomphys.2024.105298","url":null,"abstract":"<div><p>We establish analogs of the Darboux, Moser and Weinstein theorems for prequantum systems. We show that two prequantum systems on a manifold with vanishing first cohomology, with symplectic forms defining the same cohomology class and homotopic to each other within that class, differ only by a symplectomorphism and a gauge transformation. As an application, we show that the Bohr-Sommerfeld quantization of a prequantum system on a manifold with trivial first cohomology is independent of the choice of the connection.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"206 ","pages":"Article 105298"},"PeriodicalIF":1.6,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0393044024001992/pdfft?md5=fd11799b30cc96e8079ea5c1ed64ea67&pid=1-s2.0-S0393044024001992-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142088252","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Physics and geometry from a Lagrangian: Dirac spinors on a generalised frame bundle 从拉格朗日看物理和几何：广义框架束上的狄拉克旋量
IF 1.6 3区 数学
Journal of Geometry and Physics Pub Date : 2024-08-22 DOI: 10.1016/j.geomphys.2024.105297
Jérémie Pierard de Maujouy
{"title":"Physics and geometry from a Lagrangian: Dirac spinors on a generalised frame bundle","authors":"Jérémie Pierard de Maujouy","doi":"10.1016/j.geomphys.2024.105297","DOIUrl":"10.1016/j.geomphys.2024.105297","url":null,"abstract":"<div><p>We clarify the structure obtained in Hélein and Vey's proposition for a variational principle for the Einstein-Cartan gravitation formulated on a frame bundle, starting from a structure-less differentiable 10-manifold <span><span>[17]</span></span>. The obtained structure is locally equivalent to a frame bundle thus we term it “generalised frame bundle”. In the same time, we enrich the model with a Dirac spinor coupled to the Einstein-Cartan spacetime. The obtained variational equations generalise the usual Einstein-Cartan-Dirac field equations in the sense that they are shown to imply the usual field equations when the generalised frame bundle is a standard frame bundle.</p></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"206 ","pages":"Article 105297"},"PeriodicalIF":1.6,"publicationDate":"2024-08-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142096289","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
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