Journal of Geometry and Physics最新文献

{"title":"New invariants of singularities in terms of higher Nash blow-up local algebras","authors":"Shuanghe Fan ,&nbsp;Naveed Hussain ,&nbsp;Stephen S.-T. Yau ,&nbsp;Huaiqing Zuo","doi":"10.1016/j.geomphys.2025.105592","DOIUrl":"10.1016/j.geomphys.2025.105592","url":null,"abstract":"<div><div>Let <span><math><mo>(</mo><mi>V</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span> be an isolated hypersurface singularity. In our previous work, we introduced a series of new local algebras called higher Nash blow-up local algebras associated with <span><math><mo>(</mo><mi>V</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>. Thus many new invariants were introduced from these local algebras of <span><math><mo>(</mo><mi>V</mi><mo>,</mo><mn>0</mn><mo>)</mo></math></span>. We conjectured that singularities can be distinguished by a finite subset of these invariants. Furthermore, we proposed a generalized Halperin Conjecture. In this paper, we determine these invariants for simple curve singularities. As a result, we verify our conjecture for simple curve singularities. In the proof, we concretely compute the new invariants of simple curve singularities. Moreover, we verify the generalized Halperin Conjecture in some new cases.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105592"},"PeriodicalIF":1.6,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631668","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":"Gluing formulae for heat kernels","authors":"Pavel Mnev ,&nbsp;Konstantin Wernli","doi":"10.1016/j.geomphys.2025.105594","DOIUrl":"10.1016/j.geomphys.2025.105594","url":null,"abstract":"<div><div>We state and prove two gluing formulae for the heat kernel of the Laplacian on a Riemannian manifold of the form <span><math><msub><mrow><mi>M</mi></mrow><mrow><mn>1</mn></mrow></msub><msub><mrow><mo>∪</mo></mrow><mrow><mi>γ</mi></mrow></msub><msub><mrow><mi>M</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>. We present several examples.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105594"},"PeriodicalIF":1.6,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144695263","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":"Twins in Kähler and Sasaki geometry","authors":"Charles P. Boyer ,&nbsp;Hongnian Huang ,&nbsp;Eveline Legendre ,&nbsp;Christina W. Tønnesen-Friedman","doi":"10.1016/j.geomphys.2025.105591","DOIUrl":"10.1016/j.geomphys.2025.105591","url":null,"abstract":"<div><div>We introduce the notions of weighted extremal Kähler twins together with the related notion of extremal Sasaki twins. In the Kähler setting this leads to a generalization of the twinning phenomenon appearing among LeBrun's strongly Hermitian solutions to the Einstein-Maxwell equations on the first Hirzebruch surface <span><span>[36]</span></span> to weighted extremal metrics on Hirzebruch surfaces in general. We discover that many twins appear and that this can be viewed in the Sasaki setting as a case where we have more than one extremal ray in the Sasaki cone even when we do not allow changes within the isotopy class. We also study extremal Sasaki twins directly in the Sasaki setting with a main focus on the toric Sasaki case.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105591"},"PeriodicalIF":1.6,"publicationDate":"2025-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631667","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":"Geodesic causality in Kerr spacetimes with |a| ≥ M","authors":"Giulio Sanzeni ,&nbsp;Karim Mosani","doi":"10.1016/j.geomphys.2025.105589","DOIUrl":"10.1016/j.geomphys.2025.105589","url":null,"abstract":"<div><div>The analytic extension of the Kerr spacetimes into the negative radial region contains closed causal curves for any non-zero rotation parameter <em>a</em> and mass parameter <em>M</em>. Furthermore, the spacetimes become totally vicious when <span><math><mo>|</mo><mi>a</mi><mo>|</mo><mo>&gt;</mo><mi>M</mi></math></span>, meaning that through every point there exists a closed timelike curve. Despite this, we prove that Kerr spacetimes do not admit any closed null geodesics when <span><math><mo>|</mo><mi>a</mi><mo>|</mo><mo>≥</mo><mi>M</mi></math></span>. This result generalises recent findings by one of the authors, which showed the nonexistence of closed causal geodesics in the case <span><math><mo>|</mo><mi>a</mi><mo>|</mo><mo>&lt;</mo><mi>M</mi></math></span>. Combining these results, we establish the absence of closed null geodesics in Kerr spacetimes for any non-zero <em>a</em>.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105589"},"PeriodicalIF":1.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144580269","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":"Gromov-Hausdorff convergence of metric spaces of UCP maps","authors":"Tirthankar Bhattacharyya,&nbsp;Ritul Duhan,&nbsp;Chandan Pradhan","doi":"10.1016/j.geomphys.2025.105588","DOIUrl":"10.1016/j.geomphys.2025.105588","url":null,"abstract":"<div><div>It is shown that van Suijlekom's technique of imposing a set of conditions on operator system spectral triples ensures Gromov-Hausdorff convergence of sequences of sets of unital completely positive maps (equipped with the BW-topology which is metrizable). This implies that even when only a part of the spectrum of the Dirac operator is available together with a certain truncation of the <span><math><msup><mrow><mi>C</mi></mrow><mrow><mo>⁎</mo></mrow></msup></math></span>-algebra, information about the geometry can be extracted.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105588"},"PeriodicalIF":1.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633114","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":"Curvature of an exotic 7-sphere","authors":"David S. Berman ,&nbsp;Martin Cederwall ,&nbsp;Tancredi Schettini Gherardini","doi":"10.1016/j.geomphys.2025.105590","DOIUrl":"10.1016/j.geomphys.2025.105590","url":null,"abstract":"<div><div>We study the geometry of the Gromoll–Meyer sphere, one of Milnor's exotic 7-spheres. We focus on a Kaluza–Klein Ansatz, with a round <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span> as base space, unit <span><math><msup><mrow><mi>S</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span> as fibre, and <span><math><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span> <span><math><mi>S</mi><mi>U</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span> instantons as gauge fields, where all quantities admit an elegant description in quaternionic language. The metric's moduli space coincides with the <span><math><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn></math></span> instantons' moduli space quotiented by the isometry of the base, plus an additional <span><math><msup><mrow><mi>R</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span> factor corresponding to the radius of the base, <em>r</em>. We identify a “center” of the <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> instanton moduli space with enhanced symmetry. This <span><math><mi>k</mi><mo>=</mo><mn>2</mn></math></span> solution is used together with the maximally symmetric <span><math><mi>k</mi><mo>=</mo><mn>1</mn></math></span> solution to obtain a metric of maximal isometry, <span><math><mi>S</mi><mi>O</mi><mo>(</mo><mn>3</mn><mo>)</mo><mo>×</mo><mi>O</mi><mo>(</mo><mn>2</mn><mo>)</mo></math></span>, and to explicitly compute its Ricci tensor. This allows us to put a bound on <em>r</em> to ensure positive Ricci curvature, which implies various energy conditions for an 8-dimensional static space-time. This construction then enables a concrete examination of the properties of the sectional curvature.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105590"},"PeriodicalIF":1.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631665","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":"Kac-Moody algebras on soft group manifolds","authors":"Rutwig Campoamor-Stursberg ,&nbsp;Alessio Marrani ,&nbsp;Michel Rausch de Traubenberg","doi":"10.1016/j.geomphys.2025.105587","DOIUrl":"10.1016/j.geomphys.2025.105587","url":null,"abstract":"<div><div>Within the so-called group geometric approach to (super)gravity and (super)string theories, any compact Lie group manifold <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> can be smoothly deformed into a group manifold <span><math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow><mrow><mi>μ</mi></mrow></msubsup></math></span> (locally diffeomorphic to <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span> itself), which is ‘soft’, namely, based on a non-left-invariant, intrinsic one-form Vielbein <em>μ</em>, which violates the Maurer-Cartan equations and consequently has a non-vanishing associated curvature two-form. Within the framework based on the above deformation (‘softening’), we show how to construct an infinite-dimensional (infinite-rank), generalized Kac-Moody (KM) algebra associated to <span><math><msubsup><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow><mrow><mi>μ</mi></mrow></msubsup></math></span>, starting from the generalized KM algebras associated to <span><math><msub><mrow><mi>G</mi></mrow><mrow><mi>c</mi></mrow></msub></math></span>. As an application, we consider KM algebras associated to deformed manifolds such as the ‘soft’ circle, the ‘soft’ two-sphere and the ‘soft’ three-sphere. While the generalized KM algebra associated to the deformed circle is trivially isomorphic to its undeformed analogue, and hence not new, the ‘softening’ of the two- and three-sphere includes squashed manifolds (and in particular, the so-called Berger three-sphere) and yields to non-trivial results.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105587"},"PeriodicalIF":1.6,"publicationDate":"2025-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631666","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":"On invariants of families of lemniscate motions in the two-center problem","authors":"Hanna Häußler ,&nbsp;Seongchan Kim","doi":"10.1016/j.geomphys.2025.105583","DOIUrl":"10.1016/j.geomphys.2025.105583","url":null,"abstract":"<div><div>We determine four topological invariants introduced by Cieliebak-Frauenfelder-Zhao <span><span>[3]</span></span>, based on Arnold's <span><math><msup><mrow><mi>J</mi></mrow><mrow><mo>+</mo></mrow></msup></math></span>-invariant, of periodic lemniscate motions in Euler's two-center problem.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105583"},"PeriodicalIF":1.6,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631663","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":"Some computations on trivial canonical-bundle solvmanifolds","authors":"Lapo Rubini","doi":"10.1016/j.geomphys.2025.105586","DOIUrl":"10.1016/j.geomphys.2025.105586","url":null,"abstract":"<div><div>We compute the Dolbeault and the Bott-Chern cohomology of six dimensional solvmanifolds endowed with a complex structure of splitting type, introduced by Kasuya, and with trivial canonical bundle. We build, following results by Angella and Kasuya, finite dimensional double subcomplexes <span><math><mo>(</mo><msubsup><mrow><mi>C</mi></mrow><mrow><mi>Γ</mi></mrow><mrow><mo>•</mo><mo>,</mo><mo>•</mo></mrow></msubsup><mo>,</mo><mo>∂</mo><mo>,</mo><mover><mrow><mo>∂</mo></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo><mo>⊆</mo><mo>(</mo><msup><mrow><mo>∧</mo></mrow><mrow><mo>•</mo><mo>,</mo><mo>•</mo></mrow></msup><mi>G</mi><mo>/</mo><mi>Γ</mi><mo>,</mo><mo>∂</mo><mo>,</mo><mover><mrow><mo>∂</mo></mrow><mrow><mo>¯</mo></mrow></mover><mo>)</mo></math></span> for which the inclusion is an isomorphism in cohomology. We decompose such double complexes into indecomposable ones. Lastly, we study some notions of formality for this class of manifolds, giving a characterization of the <span><math><mo>∂</mo><mover><mrow><mo>∂</mo></mrow><mrow><mo>¯</mo></mrow></mover></math></span>-Lemma property in general complex dimension, and we compute triple ABC-Massey products on them.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105586"},"PeriodicalIF":1.6,"publicationDate":"2025-07-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144631664","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":"Matrix Lax pairs under the gauge equivalence relation induced by the gauge group action and Miura-type transformations for lattice equations","authors":"Sergei Igonin","doi":"10.1016/j.geomphys.2025.105585","DOIUrl":"10.1016/j.geomphys.2025.105585","url":null,"abstract":"<div><div>In this paper we explore interconnections of differential-difference matrix Lax representations (Lax pairs), gauge transformations, and discrete Miura-type transformations (MTs), which belong to the main tools in the theory of integrable differential-difference (lattice) equations.</div><div>For a given equation, two matrix Lax representations (MLRs) are said to be gauge equivalent if one of them can be obtained from the other by means of a (local) matrix gauge transformation. Matrix gauge transformations constitute an infinite-dimensional group called the matrix gauge group, which acts naturally on the set of MLRs of a given equation. Two MLRs are gauge equivalent if and only if they belong to the same orbit of the matrix gauge group action.</div><div>For a wide class of MLRs of (vector) evolutionary differential-difference equations, we present results on the following questions:<ul><li><span>1.</span><span><div>When and how can one simplify a given MLR by matrix gauge transformations and bring the MLR to a form suitable for constructing MTs?</div></span></li><li><span>2.</span><span><div>A MLR is called fake if it is gauge equivalent to a trivial MLR. How to determine whether a given MLR is not fake?</div></span></li></ul></div><div>Here and in a different publication (with E. Chistov), we apply results of the present paper to the following integrable examples:<ul><li><span>•</span><span><div>a 3-component lattice introduced by D. Zhang and D. Chen in their work on Hamiltonian structures of evolutionary lattice equations <span><span>[28]</span></span>,</div></span></li><li><span>•</span><span><div>some rational 1-component equations of order <span><math><mo>(</mo><mo>−</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></span> related to the Narita–Itoh–Bogoyavlensky lattice,</div></span></li><li><span>•</span><span><div>the 2-component Boussinesq lattice related to the lattice <span><math><msub><mrow><mi>W</mi></mrow><mrow><mn>3</mn></mrow></msub></math></span>-algebra,</div></span></li><li><span>•</span><span><div>a 2-component equation (introduced by G. Marí Beffa and Jing Ping Wang in their work on Hamiltonian evolutions of polygons <span><span>[2]</span></span>) which describes the evolution induced on invariants by an invariant evolution of planar polygons.</div></span></li></ul> This allows us to construct new integrable equations (with new MLRs) connected by new MTs to known equations.</div></div>","PeriodicalId":55602,"journal":{"name":"Journal of Geometry and Physics","volume":"216 ","pages":"Article 105585"},"PeriodicalIF":1.6,"publicationDate":"2025-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144569977","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}