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Knot groups, quandle extensions and orderability 结群、Qandle 扩展和有序性
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-29 DOI: 10.1007/s10711-023-00876-x
Idrissa Ba, Mohamed Elhamdadi
{"title":"Knot groups, quandle extensions and orderability","authors":"Idrissa Ba, Mohamed Elhamdadi","doi":"10.1007/s10711-023-00876-x","DOIUrl":"https://doi.org/10.1007/s10711-023-00876-x","url":null,"abstract":"<p>This paper gives a new way of characterizing L-space 3-manifolds by using orderability of quandles. Hence, this answers a question of Clay et al. (Question 1.1 of Can Math Bull 59(3):472–482, 2016). We also investigate both the orderability and circular orderability of dynamical extensions of orderable quandles. We give conditions under which the conjugation quandle on a group, as an extension of the conjugation of a bi-orderable group by the conjugation of a right orderable group, is right orderable. We also study the right circular orderability of link quandles. We prove that the <i>n</i>-quandle <span>(Q_n(L))</span> of the link quandle of a link <i>L</i> in the 3-sphere is not right circularly orderable and hence it is not right orderable. But on the other hand, we show that there are infinitely many links for which the <i>p</i>-enveloping group of the link quandle is right circularly orderable for any prime integer <i>p</i>.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"25 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139061686","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Median quasimorphisms on $${{,mathrm{{CAT}},}}(0)$$ cube complexes and their cup products $${{,mathrm{{CAT}},}}(0)$$立方复合物上的中值准变形及其杯积
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-23 DOI: 10.1007/s10711-023-00870-3
Benjamin Brück, Francesco Fournier-Facio, Clara Löh
{"title":"Median quasimorphisms on $${{,mathrm{{CAT}},}}(0)$$ cube complexes and their cup products","authors":"Benjamin Brück, Francesco Fournier-Facio, Clara Löh","doi":"10.1007/s10711-023-00870-3","DOIUrl":"https://doi.org/10.1007/s10711-023-00870-3","url":null,"abstract":"<p>Cup products provide a natural approach to access higher bounded cohomology groups. We extend vanishing results on cup products of Brooks quasimorphisms of free groups to cup products of median quasimorphisms, i.e., Brooks-type quasimorphisms of group actions on <span>({{,mathrm{{CAT}},}}(0))</span> cube complexes. In particular, we obtain such vanishing results for groups acting on trees and for right-angled Artin groups. Moreover, we outline potential applications of vanishing results for cup products in bounded cohomology.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"89 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139029383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Relations with a fixed interval exchange transformation 具有固定间隔交换变换的关系
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-15 DOI: 10.1007/s10711-023-00868-x
Magali Jay
{"title":"Relations with a fixed interval exchange transformation","authors":"Magali Jay","doi":"10.1007/s10711-023-00868-x","DOIUrl":"https://doi.org/10.1007/s10711-023-00868-x","url":null,"abstract":"<h3>Abstract</h3> <p>We study the group of all interval exchange transformations (IETs). Katok asked whether it contains a free subgroup. We show that for every IET <em>S</em>, there exists a dense open set <span> <span>(Omega (S))</span> </span> of admissible IETs such that the group generated by <em>S</em> and any <span> <span>(Tin Omega (S))</span> </span> is not free of rank 2. This extends a result by Dahmani et al. (Groups Geom Dyn 7(4):883–910, 2013): the group generated by a generic pair of elements of IET([0;1)) is not free (assuming a suitable condition on the underlying permutation).</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"295 2 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138687579","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Correction: An improved bound on the optimal paper Moebius band 更正：最佳纸质莫比乌斯带的改进约束
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-13 DOI: 10.1007/s10711-023-00869-w
Richard Evan Schwartz
{"title":"Correction: An improved bound on the optimal paper Moebius band","authors":"Richard Evan Schwartz","doi":"10.1007/s10711-023-00869-w","DOIUrl":"https://doi.org/10.1007/s10711-023-00869-w","url":null,"abstract":"","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"195 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138578926","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Moduli spaces of polygons and deformations of polyhedra with boundary 多边形的模空间和有边界多面体的变形
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-13 DOI: 10.1007/s10711-023-00834-7
Sasha Anan’in, Dmitrii Korshunov
{"title":"Moduli spaces of polygons and deformations of polyhedra with boundary","authors":"Sasha Anan’in, Dmitrii Korshunov","doi":"10.1007/s10711-023-00834-7","DOIUrl":"https://doi.org/10.1007/s10711-023-00834-7","url":null,"abstract":"<p>We prove a conjecture of Ian Agol: all isometric realizations of a polyhedral surface with boundary sweep out an isotropic subset in the Kapovich-Millson moduli space of polygons isomorphic to the boundary. For a generic polyhedral disk we show that boundaries of its isometric realizations make up a Lagrangian subset. As an application of this result, we conclude that a generic equilateral polygon cannot be domed (in the sense of a problem of Kenyon, Glazyrin and Pak).</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"10 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138578924","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Vanishing theorem on parabolic Kähler manifolds 凯勒抛物流形上的消失定理
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-13 DOI: 10.1007/s10711-023-00872-1
Teng Huang
{"title":"Vanishing theorem on parabolic Kähler manifolds","authors":"Teng Huang","doi":"10.1007/s10711-023-00872-1","DOIUrl":"https://doi.org/10.1007/s10711-023-00872-1","url":null,"abstract":"<p>In this article, we consider the semipositive (resp. nef) line bundle on compact Kähler parabolic (resp. hyperbolic) manifolds. We prove some vanishing theorems for the <span>(L^{2})</span>-harmonic (<i>n</i>, <i>q</i>)-form of the holomorphic line bundles over complete Kähler manifolds.</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"21 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138579028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Low dilatation pseudo-Anosovs on punctured surfaces and volume. 穿刺表面和体积上的低膨胀伪阿诺索夫。
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-09 DOI: 10.1007/s10711-023-00860-5
Shixuan Li
{"title":"Low dilatation pseudo-Anosovs on punctured surfaces and volume.","authors":"Shixuan Li","doi":"10.1007/s10711-023-00860-5","DOIUrl":"https://doi.org/10.1007/s10711-023-00860-5","url":null,"abstract":"<p>For a pseudo-Anosov homeomorphism <i>f</i> on a closed surface of genus <span>(gge 2)</span>, for which the entropy is on the order <span>(frac{1}{g})</span> (the lowest possible order), Farb-Leininger-Margalit showed that the volume of the mapping torus is bounded, independent of <i>g</i>. We show that the analogous result fails for a surface of fixed genus <i>g</i> with <i>n</i> punctures, by constructing pseudo-Anosov homeomorphism with entropy of the minimal order <span>(frac{log n}{n})</span>, and volume tending to infinity.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"248 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Harmonic maps between 2-dimensional simplicial complexes: conformal and singular metrics 二维单纯复数之间的谐波映射：共形和奇异度量
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-12-09 DOI: 10.1007/s10711-023-00871-2
Brian Freidin, Victòria Gras Andreu
{"title":"Harmonic maps between 2-dimensional simplicial complexes: conformal and singular metrics","authors":"Brian Freidin, Victòria Gras Andreu","doi":"10.1007/s10711-023-00871-2","DOIUrl":"https://doi.org/10.1007/s10711-023-00871-2","url":null,"abstract":"<p>We study metrics on two-dimensional simplicial complexes that are conformal either to flat Euclidean metrics or to the ideal hyperbolic metrics described by Charitos and Papadopoulos. Extending the results of our previous paper, we prove existence, uniqueness, and regularity results for harmonic maps between two such metrics on a complex.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"179 1","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-12-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138560422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Inversion maps and torus actions on rational homogeneous varieties 有理齐次变异上的反演映射和环面作用
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-11-29 DOI: 10.1007/s10711-023-00866-z
Alberto Franceschini, Luis E. Solá Conde
{"title":"Inversion maps and torus actions on rational homogeneous varieties","authors":"Alberto Franceschini, Luis E. Solá Conde","doi":"10.1007/s10711-023-00866-z","DOIUrl":"https://doi.org/10.1007/s10711-023-00866-z","url":null,"abstract":"<p>Complex projective algebraic varieties with <span>({{mathbb {C}}}^*)</span>-actions can be thought of as geometric counterparts of birational transformations. In this paper we describe geometrically the birational transformations associated to rational homogeneous varieties endowed with a <span>({{mathbb {C}}}^*)</span>-action with no proper isotropy subgroups.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"28 24","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 a convexity property of the space of almost fuchsian immersions 关于几乎紫红色浸没空间的凸性
IF 0.5 4区 数学
Geometriae Dedicata Pub Date : 2023-11-28 DOI: 10.1007/s10711-023-00865-0
Samuel Bronstein, Graham Andrew Smith
{"title":"On a convexity property of the space of almost fuchsian immersions","authors":"Samuel Bronstein, Graham Andrew Smith","doi":"10.1007/s10711-023-00865-0","DOIUrl":"https://doi.org/10.1007/s10711-023-00865-0","url":null,"abstract":"<p>We study the space of Hopf differentials of almost fuchsian minimal immersions of compact Riemann surfaces. We show that the extrinsic curvature of the immersion at any given point is a concave function of the Hopf differential. As a consequence, we show that the set of all such Hopf differentials is a convex subset of the space of holomorphic quadratic differentials of the surface. In addition, we address the non-equivariant case, and obtain lower and upper bounds for the size of this set.\u0000</p>","PeriodicalId":55103,"journal":{"name":"Geometriae Dedicata","volume":"30 12","pages":""},"PeriodicalIF":0.5,"publicationDate":"2023-11-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138504919","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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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