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Pacific Journal of Mathematics最新文献

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Bridge trisections and classical knotted surface theory 桥三分体与经典结面理论
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-12-21 DOI: 10.2140/pjm.2022.319.343
Jason Joseph, J. Meier, Maggie Miller, Alexander Zupan
{"title":"Bridge trisections and classical knotted surface theory","authors":"Jason Joseph, J. Meier, Maggie Miller, Alexander Zupan","doi":"10.2140/pjm.2022.319.343","DOIUrl":"https://doi.org/10.2140/pjm.2022.319.343","url":null,"abstract":"We seek to connect ideas in the theory of bridge trisections with other well-studied facets of classical knotted surface theory. First, we show how the normal Euler number can be computed from a tri-plane diagram, and we use this to give a trisection-theoretic proof of the Whitney-Massey Theorem, which bounds the possible values of this number in terms of the Euler characteristic. Second, we describe in detail how to compute the fundamental group and related invariants from a tri-plane diagram, and we use this, together with an analysis of bridge trisections of ribbon surfaces, to produce an infinite family of knotted spheres that admit non-isotopic bridge trisections of minimal complexity.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48501151","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: 8
Weyl estimates for spacelike hypersurfaces in de Sitter space de Sitter空间中类空间超曲面的Weyl估计
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-12-21 DOI: 10.2140/pjm.2022.320.1
Daniel Ballesteros-Chavez, W. Klingenberg, Ben Lambert
{"title":"Weyl estimates for spacelike hypersurfaces in de Sitter space","authors":"Daniel Ballesteros-Chavez, W. Klingenberg, Ben Lambert","doi":"10.2140/pjm.2022.320.1","DOIUrl":"https://doi.org/10.2140/pjm.2022.320.1","url":null,"abstract":". We study the isometric spacelike embedding problem in scaled de Sitter space, and obtain Weyl-type estimates and the corresponding closedness in the space of embeddings.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43479448","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
Coarse geometry of Hecke pairs and theBaum–Connes conjecture Hecke对的粗糙几何和baum - connes猜想
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-12-19 DOI: 10.2140/pjm.2023.322.21
Cl'ement Dell'Aiera
{"title":"Coarse geometry of Hecke pairs and the\u0000Baum–Connes conjecture","authors":"Cl'ement Dell'Aiera","doi":"10.2140/pjm.2023.322.21","DOIUrl":"https://doi.org/10.2140/pjm.2023.322.21","url":null,"abstract":"We study Hecke pairs using the coarse geometry of their coset space and their Schlichting completion. We prove new stability results for the Baum-Connes and the Novikov conjectures in the case where the pair is co-Haagerup. This allows to generalize previous results, while providing new examples of groups satisfying the Baum-Connes conjecture with coefficients. For instance, we show that for some S-arithmetic subgroups of Sp(5,1) and Sp(3,1) the conjecture with coefficients holds.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44379227","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
The index of a modular differential operator 模微分算子的指数
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-12-13 DOI: 10.2140/pjm.2021.315.45
W. Duke
{"title":"The index of a modular differential operator","authors":"W. Duke","doi":"10.2140/pjm.2021.315.45","DOIUrl":"https://doi.org/10.2140/pjm.2021.315.45","url":null,"abstract":"The space of all weakly holomorphic modular forms and the space of all holomorphic period functions of a fixed weight for the modular group are realized as locally convex topological vector spaces that are topologically dual to each other. This framework is used to study the kernel and range of a linear differential operator that preserves modularity and to define and describe its adjoint. The main result is an index formula for such a differential operator that is holomorphic at infinity. The co-kernel of the operator is identified as a cohomology group of the modular group acting on the kernel.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42694080","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
Bessel quotients and Robin eigenvalues 贝塞尔商和罗宾特征值
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-12-13 DOI: 10.2140/pjm.2021.315.75
P. Freitas
{"title":"Bessel quotients and Robin eigenvalues","authors":"P. Freitas","doi":"10.2140/pjm.2021.315.75","DOIUrl":"https://doi.org/10.2140/pjm.2021.315.75","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44081923","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: 1
An algorithmic strategy for finding characteristic maps over wedged simplicial complexes 寻找楔形简单复合体特征映射的算法策略
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-11-14 DOI: 10.2140/pjm.2022.320.13
Suyoung Choi, Mathieu Vall'ee
{"title":"An algorithmic strategy for finding characteristic maps over wedged simplicial complexes","authors":"Suyoung Choi, Mathieu Vall'ee","doi":"10.2140/pjm.2022.320.13","DOIUrl":"https://doi.org/10.2140/pjm.2022.320.13","url":null,"abstract":". The puzzle method was introduced by Choi and Park as an effective method for finding non-singular characteristic maps over wedged simplicial complexes K ( J ) obtained from a given simplicial complex K . We study further the mod 2 case of the puzzle method. We firstly describe it completely in terms of linear algebraic language which allows us to develop a constructive puzzle algorithm. We also analyze our algorithm and compare its performances with other known algorithms including the Garrison and Scott algorithm.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42558482","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: 3
Derivation Lie algebras of new k-th localalgebras of isolated hypersurface singularities 孤立超表面奇点的新k-局部代数的推导李代数
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-11-10 DOI: 10.2140/pjm.2021.314.311
Naveed Hussain, S. Yau, Huaiqing Zuo
{"title":"Derivation Lie algebras of new k-th local\u0000algebras of isolated hypersurface singularities","authors":"Naveed Hussain, S. Yau, Huaiqing Zuo","doi":"10.2140/pjm.2021.314.311","DOIUrl":"https://doi.org/10.2140/pjm.2021.314.311","url":null,"abstract":". Let ( V, 0) = { ( z 1 , · · · , z n ) ∈ C n : f ( z 1 , · · · , z n ) = 0 } be an isolated hypersurface singularity with mult ( f ) = m . Let J k ( f ) be the ideal generated by all k -th order partial derivative of f . For 1 ≤ k ≤ m − 1, the new object L k ( V ) is defined to be the Lie algebra of derivations of the new k -th local algebra M k ( V ), where M k ( V ) := O n / ( f + J 1 ( f ) + · · · + J k ( f )). Its dimension is denoted as δ k ( V ). This number δ k ( V ) is a new numerical analytic invariant. In this article we compute L 3 ( V ) for fewnomial isolated singularities (binomial, trinomial) and obtain the formulas of δ 3 ( V ). We also formulate a sharp upper estimate conjecture for the δ k ( V ) of weighted homogeneous isolated hypersurface singularities and verify this conjecture for large class of singularities. Furthermore, we formulate another inequality conjecture: δ ( k +1) ( V ) < δ k ( V ) , k ≥ 1 and verify it for low-dimensional fewnomial singularities.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42555464","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: 2
The unit signature rank deficiency is unbounded over cyclotomic fields 单位签名秩缺乏性在切环场上无界
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-11-10 DOI: 10.2140/pjm.2021.314.259
D. Dummit, H. Kisilevsky
{"title":"The unit signature rank deficiency is unbounded over cyclotomic fields","authors":"D. Dummit, H. Kisilevsky","doi":"10.2140/pjm.2021.314.259","DOIUrl":"https://doi.org/10.2140/pjm.2021.314.259","url":null,"abstract":"","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43914084","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: 2
On the Chow groups of a biquaternionSeveri–Brauer variety 双四元数severi - brauer品种的Chow群
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-31 DOI: 10.2140/pjm.2022.321.359
Eoin Mackall
{"title":"On the Chow groups of a biquaternion\u0000Severi–Brauer variety","authors":"Eoin Mackall","doi":"10.2140/pjm.2022.321.359","DOIUrl":"https://doi.org/10.2140/pjm.2022.321.359","url":null,"abstract":"We provide an alternative proof that the Chow group of $1$-cycles on a Severi--Brauer variety associated to a biquaternion division algebra is torsion-free. There are three proofs of this result in the literature, all of which are due to Karpenko and rely on a clever use of $K$-theory. The proof that we give here, by contrast, is geometric and uses degenerations of quartic elliptic normal curves.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45818265","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
Ostrowski quotients for finite extensions of number fields 数域有限扩展的Ostrowski商
IF 0.6 3区 数学
Pacific Journal of Mathematics Pub Date : 2021-10-31 DOI: 10.2140/pjm.2022.321.415
Ehsan Shahoseini, A. Rajaei, A. Maarefparvar
{"title":"Ostrowski quotients for finite extensions of number fields","authors":"Ehsan Shahoseini, A. Rajaei, A. Maarefparvar","doi":"10.2140/pjm.2022.321.415","DOIUrl":"https://doi.org/10.2140/pjm.2022.321.415","url":null,"abstract":"For $L/K$ a finite Galois extension of number fields, the relative P'olya group $Po(L/K)$ coincides with the group of strongly ambiguous ideal classes in $L/K$. In this paper, using a well known exact sequence related to $Po(L/K)$, in the works of Brumer-Rosen and Zantema, we find short proofs for some classical results in the literatur. Then we define the ``Ostrowski quotient'' $Ost(L/K)$ as the cokernel of the capitulation map into $Po(L/K)$, and generalize some known results for $Po(L/mathbb{Q})$ to $Ost(L/K)$.","PeriodicalId":54651,"journal":{"name":"Pacific Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.6,"publicationDate":"2021-10-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42229788","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: 3
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