Journal of Geometry and Physics最新文献

{"title":"Cohomologically symplectic structures on stratified spaces","authors":"Xiangdong Yang","doi":"10.1016/j.geomphys.2026.105795","DOIUrl":"10.1016/j.geomphys.2026.105795","url":null,"abstract":"<div><div>In this paper, we introduce the notion of cohomologically symplectic structure on a differentiable stratified space, and we show that the singular symplectic quotient <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>=</mo><msup><mrow><mi>μ</mi></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mo>(</mo><mn>0</mn><mo>)</mo><mo>/</mo><mi>G</mi></math></span> of a symplectic Hamiltonian <em>G</em>-manifold <span><math><mo>(</mo><mi>M</mi><mo>,</mo><mi>ω</mi><mo>,</mo><mi>G</mi><mo>,</mo><mi>μ</mi><mo>)</mo></math></span> admits a natural cohomologically symplectic structure induced by the original symplectic structure on <em>M</em>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"224 ","pages":"Article 105795"},"PeriodicalIF":1.2,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146193180","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}

{"title":"Non-weight modules over the BMS-Kac-Moody algebra","authors":"Qiufan Chen,&nbsp;Cong Guo","doi":"10.1016/j.geomphys.2026.105797","DOIUrl":"10.1016/j.geomphys.2026.105797","url":null,"abstract":"<div><div>In this paper, we construct and classify a class of non-weight modules over the BMS-Kac-Moody algebra, which are free modules of rank one when restricted to the universal enveloping algebra of the Cartan subalgebra (modulo center). We give the classification of such modules. Moreover, the irreducibility and the isomorphism classes of these modules are determined.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"224 ","pages":"Article 105797"},"PeriodicalIF":1.2,"publicationDate":"2026-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146193181","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}

{"title":"Quantization of web geometry: Semisymmetrization of linear quantum quasigroups","authors":"Jonathan D.H. Smith","doi":"10.1016/j.geomphys.2026.105781","DOIUrl":"10.1016/j.geomphys.2026.105781","url":null,"abstract":"<div><div>Classical quasigroups coordinatize structures called 3-nets in combinatorics, and 3-webs in geometry. The coordinatization is up to isotopy, a relation coarser than isomorphism. The semisymmetrization of a classical quasigroup is built on the cube of the underlying set of the quasigroup. Isotopic quasigroups have isomorphic semisymmetrizations.</div><div>Quantum quasigroups provide a self-dual unification (with both a multiplication and a comultiplication) of quasigroups and Hopf algebras, in the general setting of symmetric monoidal categories. Linear quantum quasigroups are quantum quasigroups in categories of vector spaces or modules over a commutative ring, with the direct sum as the Cartesian monoidal product.</div><div>With a view to addressing the quantization of web geometry, the paper determines linear quantum quasigroup structures that provide comultiplications to extend the semisymmetrization multiplication of a linear quasigroup. In particular, if the linear quasigroup structure comes from a real or complex affine plane, a complete classification of the quantum semisymmetric comultiplications is provided, based on the solution of a system of cubic equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"223 ","pages":"Article 105781"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102835","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}

{"title":"Remarks on structures and preservation in forced discrete mechanical systems of Routh type","authors":"Matías I. Caruso ,&nbsp;Javier Fernández ,&nbsp;Cora Tori ,&nbsp;Marcela Zuccalli","doi":"10.1016/j.geomphys.2026.105776","DOIUrl":"10.1016/j.geomphys.2026.105776","url":null,"abstract":"<div><div>We study a type of forced discrete mechanical system <span><math><mo>(</mo><mi>Q</mi><mo>,</mo><msub><mrow><mi>L</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>,</mo><msub><mrow><mi>f</mi></mrow><mrow><mi>d</mi></mrow></msub><mo>)</mo></math></span> —that we name of Routh type— whose (discrete) time-flow preserves a symplectic structure on <span><math><mi>Q</mi><mo>×</mo><mi>Q</mi></math></span>. That structure arises as the pullback via the forced discrete Legendre transform of the canonical symplectic structure on <span><math><msup><mrow><mi>T</mi></mrow><mrow><mo>⁎</mo></mrow></msup><mi>Q</mi></math></span> modified by a “magnetic term”. One example of this type of system is provided by the Lagrangian reduction of a symmetric (unforced) discrete mechanical system in the Routh style. In this particular case, we do not reduce by the full symmetry group but, rather, by an appropriate isotropy subgroup. In this context, the preserved symplectic structure can be alternatively seen as the Marsden-Weinstein reduction of the canonical symplectic structure <span><math><msub><mrow><mi>ω</mi></mrow><mrow><msub><mrow><mi>L</mi></mrow><mrow><mi>d</mi></mrow></msub></mrow></msub></math></span> on <span><math><mi>Q</mi><mo>×</mo><mi>Q</mi></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"223 ","pages":"Article 105776"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102939","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}

{"title":"The Atiyah class of DG manifolds of amplitude +1","authors":"Seokbong Seol","doi":"10.1016/j.geomphys.2026.105774","DOIUrl":"10.1016/j.geomphys.2026.105774","url":null,"abstract":"<div><div>A DG manifold of amplitude +1 encodes the derived intersection of a section <em>s</em> and the zero section of a vector bundle <em>E</em>. In this paper, we compute the Atiyah class of DG manifolds of amplitude +1. In particular, we show that the Atiyah class vanishes if and only if the intersection of <em>s</em> with the zero section is a clean intersection. As an application, we study the Atiyah class of DG manifolds that encodes the derived intersection of two smooth manifolds.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"223 ","pages":"Article 105774"},"PeriodicalIF":1.2,"publicationDate":"2026-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146102844","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}

{"title":"Moduli spaces of pentagonal subdivision tilings","authors":"Jinjin Liang ,&nbsp;Erxiao Wang ,&nbsp;Min Yan","doi":"10.1016/j.geomphys.2026.105773","DOIUrl":"10.1016/j.geomphys.2026.105773","url":null,"abstract":"<div><div>Pentagonal subdivision gives three families of edge-to-edge tilings of the sphere by congruent pentagons. Each family forms a two real parameter moduli space. We describe these moduli spaces in detail, to complete the classification of such tilings and to facilitate potential applications in physics and other disciplines.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105773"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146090670","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}

{"title":"New rigidity of compact Willmore surfaces in S2+m","authors":"Deng-Yun Yang ,&nbsp;Hai-Ping Fu","doi":"10.1016/j.geomphys.2026.105767","DOIUrl":"10.1016/j.geomphys.2026.105767","url":null,"abstract":"<div><div>Let <em>M</em> be a compact Willmore surface in the unit sphere. Denote by <span><math><msubsup><mrow><mover><mrow><mi>h</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>α</mi></mrow></msubsup></math></span> the component of the traceless second fundamental form of <em>M</em>. We prove that if <span><math><mn>0</mn><mo>≤</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>+</mo><msub><mrow><mover><mrow><mi>λ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msub><mo>≤</mo><mi>n</mi></math></span>, where <span><math><msup><mrow><mi>ρ</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>=</mo><munder><mo>∑</mo><mrow><mi>α</mi><mo>,</mo><mi>i</mi><mo>,</mo><mi>j</mi></mrow></munder><msup><mrow><mo>(</mo><msubsup><mrow><mover><mrow><mi>h</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>α</mi></mrow></msubsup><mo>)</mo></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msub><mrow><mover><mrow><mi>λ</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mn>2</mn></mrow></msub></math></span> is the second largest eigenvalue of matrix <span><math><mo>(</mo><munder><mo>∑</mo><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></munder><msubsup><mrow><mover><mrow><mi>h</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>α</mi></mrow></msubsup><msubsup><mrow><mover><mrow><mi>h</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>i</mi><mi>j</mi></mrow><mrow><mi>β</mi></mrow></msubsup><mo>)</mo></math></span>, then <em>M</em> is either totally umbilic, <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msqrt><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msqrt><mo>)</mo><mo>×</mo><msup><mrow><mi>S</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>(</mo><msqrt><mrow><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac></mrow></msqrt><mo>)</mo></math></span>, or the Veronese surface. We also give an estimate for the first eigenvalue of the Schrödinger operator <span><math><mi>L</mi><mo>=</mo><mo>−</mo><mi>Δ</mi><mo>−</mo><msup><mrow><mi>ρ</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105767"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038565","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}

{"title":"Enumerative geometry via the moduli space of super Riemann surfaces","authors":"Paul Norbury","doi":"10.1016/j.geomphys.2025.105750","DOIUrl":"10.1016/j.geomphys.2025.105750","url":null,"abstract":"<div><div>In this paper we relate volumes of moduli spaces of super Riemann surfaces to integrals over the moduli space of stable Riemann surfaces <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></math></span>. This allows us to prove via algebraic geometry a recursion between the volumes of moduli spaces of super hyperbolic surfaces previously proven via super geometry techniques by Stanford and Witten. The recursion between the volumes of moduli spaces of super hyperbolic surfaces is proven to be equivalent to the property that a generating function for the intersection numbers of a natural collection of cohomology classes <span><math><msub><mrow><mi>Θ</mi></mrow><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></math></span> with tautological classes on <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></math></span> is a KdV tau function. This is analogous to Mirzakhani's proof of the Kontsevich-Witten theorem, which relates a generating function for the intersection numbers of tautological classes on <span><math><msub><mrow><mover><mrow><mi>M</mi></mrow><mo>‾</mo></mover></mrow><mrow><mi>g</mi><mo>,</mo><mi>n</mi></mrow></msub></math></span> to KdV, using volumes of moduli spaces of hyperbolic surfaces.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105750"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146038569","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}

{"title":"Complex-valued extension of mean curvature for surfaces in Riemann-Cartan geometry","authors":"Dongha Lee","doi":"10.1016/j.geomphys.2025.105748","DOIUrl":"10.1016/j.geomphys.2025.105748","url":null,"abstract":"<div><div>We extend the framework of submanifolds in Riemannian geometry to Riemann-Cartan geometry, which addresses connections with torsion. This procedure naturally introduces a 2-form on submanifolds associated with the nontrivial ambient torsion, whose Hodge dual plays the role of an imaginary counterpart to mean curvature for surfaces in a Riemann-Cartan 3-manifold. We observe that this complex-valued geometric quantity interacts with a number of other geometric concepts including the Hopf differential and the Gauss map, which generalizes classical minimal surface theory.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105748"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940685","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}

{"title":"Generalized hypergeometric equations and 2d TQFT for dormant opers in characteristic ≤7","authors":"Keita Mori,&nbsp;Yasuhiro Wakabayashi","doi":"10.1016/j.geomphys.2025.105747","DOIUrl":"10.1016/j.geomphys.2025.105747","url":null,"abstract":"<div><div>This note studies <span><math><msub><mrow><mi>PGL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-opers arising from generalized hypergeometric differential equations in prime characteristic <em>p</em>. We prove that these opers are rigid within the class of dormant opers. By combining this rigidity result with previous work in the enumerative geometry of dormant opers, we obtain a complete and explicit description of the 2d TQFTs that compute the number of dormant <span><math><msub><mrow><mi>PGL</mi></mrow><mrow><mi>n</mi></mrow></msub></math></span>-opers for primes <span><math><mi>p</mi><mo>≤</mo><mn>7</mn></math></span>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"222 ","pages":"Article 105747"},"PeriodicalIF":1.2,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145940687","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}