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An algorithm taking Kirby diagrams to trisection diagrams 一种将柯比图转换为三分图的算法
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-10-31 DOI: 10.2140/pjm.2022.318.109
Willi Kepplinger
We present an algorithm taking a Kirby diagram of a closed oriented $4$-manifold to a trisection diagram of the same manifold. This algorithm provides us with a large number of examples for trisection diagrams of closed oriented $4$-manifolds since many Kirby-diagrammatic descriptions of closed oriented $4$-manifolds are known. That being said, the algorithm does not necessarily provide particularly efficient trisection diagrams. We also extend this algorithm to work for the non-orientable case.
我们提出了一种算法,将一个封闭的面向$4$流形的Kirby图转化为相同流形的三切分图。该算法为我们提供了大量的面向闭合$4$流形的三角图示例,因为许多面向闭合$4$流形的kirby图描述是已知的。也就是说,该算法不一定提供特别有效的三切分图。我们还将该算法扩展到非定向情况下。
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引用次数: 4
Orders of the canonical vector bundles over configuration spaces of finite graphs 有限图构型空间上正则向量束的阶数
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-10-25 DOI: 10.2140/pjm.2022.316.53
F. Cohen, R. Huang
We prove that the order of the canonical vector bundle over the configuration space is 2 for a general planar graph, and is 4 for a nonplanar graph.
证明了构型空间上正则向量束的阶数对于一般平面图是2阶,对于非平面图是4阶。
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引用次数: 0
On the global weak solution problem of semilinear generalized Tricomi equations, II 半线性广义Tricomi方程的整体弱解问题,2
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-10-15 DOI: 10.2140/pjm.2021.314.29
Daoyin He, I. Witt, Huicheng Yin
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引用次数: 1
On totally umbilical surfaces in the warpedproduct 𝕄(κ)f× I 在弯曲产物𝕄(κ) fxi的完全脐带表面
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-10-12 DOI: 10.2140/pjm.2021.313.343
Ady Cambraia Jr., Abigail Folha, C. Peñafiel
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引用次数: 1
Isoperimetric bounds for lower-order eigenvalues 低阶特征值的等周界
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-10-05 DOI: 10.2140/pjm.2022.317.297
F. Fang, C. Xia
We adopt the convention that each eigenvalue is repeated according to its multiplicity. An important issue in spectral geometry is to obtain good estimates for these and other eigenvalues in terms of the geometric data of the manifold M such as the volume, the diameter, the curvature, the isoperimetric constants, etc. See [1],[2],[10],[13],[31] for references. On the other hand, after the seminal works of Bleecker-Weiner [4] and Reilly [30], the following approach is developed: the manifold (M, g) is immersed isometrically into another Riemannian manifold. One then gets good estimates for λk(M), mostly for λ1(M), in termos of the extrinsic geometric quantities of M . See for example [4], [15], [16], [23], [24], [35], [37]. Especially relevant for us is the quoted work of Reilly [30], where he obtained the following remarkable isoperimetric inequality for the first positive eigenvalue λ1(M) in the case that M is embedded as a hypersurface bounding a domain Ω in R: λ1(M) ≤ n− 1 n2 · |M | 2 |Ω|2 . (1.1)
我们采用了每个特征值根据其多重性重复的约定。谱几何中的一个重要问题是根据流形M的几何数据,如体积、直径、曲率、等周常数等,获得这些特征值和其他特征值的良好估计。参考文献见[1]、[2]、[10]、[13]、[31]。另一方面,在Bleecker Weiner[4]和Reilly[30]的开创性工作之后,发展了以下方法:将流形(M,g)等距地浸入另一个黎曼流形中。然后,根据M的外在几何量,可以得到λk(M)的良好估计,主要是λ1(M)。参见例如[4]、[15]、[16]、[23]、[24]、[35]、[37]。特别与我们相关的是Reilly[30]的引用工作,其中他在M嵌入为R中的域Ω的超曲面的情况下,获得了第一个正特征值λ1(M)的以下显著等周不等式:λ1(M)≤n−1 n2·|M|2|Ω|2。(1.1)
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引用次数: 0
Representations of orientifoldKhovanov–Lauda–Rouquier algebras and the Enomoto–Kashiwara algebra OrientalifoldKhovanov–Lauda–Rouquier代数和Enomoto–Kashiwara代数的表示
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-10-04 DOI: 10.2140/pjm.2023.322.407
T. Przeździecki
We consider an"orientifold"generalization of Khovanov-Lauda-Rouquier algebras, depending on a quiver with an involution and a framing. Their representation theory is related, via a Schur-Weyl duality type functor, to Kac-Moody quantum symmetric pairs, and, via a categorification theorem, to highest weight modules over an algebra introduced by Enomoto and Kashiwara. Our first main result is a new shuffle realization of these highest weight modules and a combinatorial construction of their PBW and canonical bases in terms of Lyndon words. Our second main result is a classification of irreducible representations of orientifold KLR algebras and a computation of their global dimension in the case when the framing is trivial.
我们考虑了Khovanov-Lauda-Rouquier代数的“方向性”推广,它依赖于一个有对合和分幅的颤振。通过Schur-Weyl对偶型泛子,他们的表示理论与Kac-Moody量子对称对有关,并通过分类定理与Enomoto和Kashiwara引入的代数上的最高权模有关。我们的第一个主要结果是对这些权重最高的模块进行了新的洗牌实现,并根据Lyndon词组合构建了它们的PBW和规范基。我们的第二个主要结果是对东方可折KLR代数的不可约表示进行了分类,并计算了它们在框架平凡情况下的整体维数。
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引用次数: 2
A note on the two-dimensional Lagrangian mean curvature equation 关于二维拉格朗日平均曲率方程的注解
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-10-04 DOI: 10.2140/pjm.2022.318.43
A. Bhattacharya
In this note, we use Warren-Yuan's super isoperimetric inequality on the level sets of subharmonic functions, which is available only in two dimensions, to derive a modified Hessian bound for solutions of the two dimensional Lagrangian mean curvature equation. We assume the Lagrangian phase to be supercritical with bounded second derivatives. Unlike the previous approach, the simplified approach in this proof does not require the Michael-Simon mean value and Sobolev inequalities on generalized submanifolds of $mathbb{R}^n$.
本文利用只存在于二维的次调和函数水平集上的Warren-Yuan超等周不等式,导出了二维拉格朗日平均曲率方程解的修正Hessian界。我们假设二阶导数有界的拉格朗日相是超临界的。与先前的方法不同,本证明中的简化方法不需要$mathbb{R}^n$的广义子流形上的Michael-Simon均值和Sobolev不等式。
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引用次数: 3
Connected components of Morse boundaries of graphs of groups 群图的莫尔斯边界的连通分量
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-09-24 DOI: 10.2140/pjm.2022.317.339
Elia Fioravanti, Annette Karrer
Let a finitely generated group $G$ split as a graph of groups. If edge groups are undistorted and do not contribute to the Morse boundary $partial_MG$, we show that every connected component of $partial_MG$ with at least two points originates from the Morse boundary of a vertex group. Under stronger assumptions on the edge groups (such as wideness in the sense of Druc{t}u-Sapir), we show that Morse boundaries of vertex groups are topologically embedded in $partial_MG$.
设一个有限生成的群$G$分裂为群的图。如果边群未变形且不构成Morse边界$partial_MG$,我们证明了$partial_MG$中每一个至少有两个点的连通分量都起源于顶点群的Morse边界。在更强的边群假设下(如Druc{t}u-Sapir意义上的宽度),我们证明了顶点群的Morse边界拓扑嵌入在$partial_MG$中。
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引用次数: 1
A coarse geometric expansion of a variant ofArthur’s truncated traces and some applications 阿瑟截断迹的一种变体的粗略几何展开及其一些应用
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-09-21 DOI: 10.2140/pjm.2022.321.193
Hongjie Yu
Let F be a global function field with constant field $mathbb{F}_q$. Let G be a reductive group over $mathbb{F}_q$. We establish a variant of Arthur's truncated kernel for G and for its Lie algebra which generalizes Arthur's original construction. We establish a coarse geometric expansion for our variant truncation. As applications, we consider some existence and uniqueness problems of some cuspidal automorphic representations for the functions field of the projective line $mathbb{P}^1_{mathbb{F}_q}$ with two points of ramifications.
设F为一个具有恒定域$mathbb{F}_q$的全局函数域。设G是$mathbb{F}_q$上的约简群。我们为G及其李代数建立了Arthur截断核的一个变体,它推广了Arthur的原始构造。我们建立了变量截断的粗几何展开式。作为应用,我们研究了具有两点分支的射影线$mathbb{P}^1_{mathbb{F}_q}$的函数域的一些逆自同态表示的存在唯一性问题。
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引用次数: 1
Local exterior square and Asai L-functions forGL(n) in odd characteristic 局部外方阵与Asai l -函数forGL(n)的奇特征
IF 0.6 3区 数学 Q2 MATHEMATICS Pub Date : 2021-09-13 DOI: 10.2140/pjm.2023.322.301
Yeongseong Jo
Let $F$ be a non-archimedean local field of odd characteristic $p>0$. In this paper, we consider local exterior square $L$-functions $L(s,pi,wedge^2)$, Bump-Friedberg $L$-functions $L(s,pi,BF)$, and Asai $L$-functions $L(s,pi,As)$ of an irreducible admissible representation $pi$ of $GL_m(F)$. In particular, we establish that those $L$-functions, via the theory of integral representations, are equal to their corresponding Artin $L$-functions $L(s,wedge^2(phi(pi)))$, $L(s+1/2,phi(pi))L(s,wedge^2(phi(pi)))$, and $L(s,As(phi(pi)))$ of the associated Langlands parameter $phi(pi)$ under the local Langlands correspondence. These are achieved by proving the identity for irreducible supercuspidal representations, exploiting the local to global argument due to Henniart and Lomeli.
设$F$是奇特征$p>0$的非阿基米德局部域。在本文中,我们考虑$GL_m(F)$的不可约可容许表示$pi$的局部外平方$L$-函数$L。特别地,我们通过积分表示理论,确定了这些$L$-函数等于它们在局部Langlands对应关系下的相关Langlands参数$phi(pi)$的相应Artin$L$-L$-函数$L(s,wedge^2(pi(pi。这些是通过利用Henniart和Lomeli提出的从局部到全局的论点来证明不可约超三尖体表示的恒等式来实现的。
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引用次数: 4
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Pacific Journal of Mathematics
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