Glasgow Mathematical Journal最新文献

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Girth Alternative for subgroups of (1)、(2)、(3)和(4)

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-05-09 DOI: 10.1017/s0017089524000181

Azer Akhmedov

We prove the Girth Alternative for finitely generated subgroups of

$PL_o(I)$

. We also prove that a finitely generated subgroup of Homeo

$_{+}(I)$

which is sufficiently rich with hyperbolic-like elements has infinite girth.

我们证明了$PL_o(I)$ 的有限生成子群的周长备选方案。我们还证明了有足够多双曲元素的有限生成的Homeo $_{+}(I)$子群具有无限周长。

引用次数: 0

Thinness of some hypergeometric groups in 一些超几何群的稀疏性在

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-05-02 DOI: 10.1017/s0017089524000168

Sandip Singh, Shashank Vikram Singh

We show the thinness of

$7$

of the

$40$

hypergeometric groups having a maximally unipotent monodromy in

$mathrm{Sp}(6)$

我们证明了$mathrm{Sp}(6)$中具有最大单势单色性的$40$超几何群中$7$的稀疏性。

引用次数: 0

Simplicial volume of manifolds with amenable fundamental group at infinity 流形的简单体积，其基本群在无穷远处是可调和的

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-04-22 DOI: 10.1017/s0017089524000107

Giuseppe Bargagnati

We show that for

$n neq 1,4$

, the simplicial volume of an inward tame triangulable open

$n$

-manifold

$M$

with amenable fundamental group at infinity at each end is finite; moreover, we show that if also

$pi _1(M)$

is amenable, then the simplicial volume of

$M$

vanishes. We show that the same result holds for finitely-many-ended triangulable manifolds which are simply connected at infinity.

我们证明，对于 $n neq 1,4$ ，每一端在无穷远处都有可简化基群的向内驯服的可三角开 $n$ -manifold $M$ 的简体积是有限的；此外，我们还证明，如果 $pi _1(M)$ 也是可简化的，那么 $M$ 的简体积就会消失。我们证明同样的结果也适用于在无穷处简单相连的有限多端可三角流形。

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引用次数: 0

Maximal subgroups of a family of iterated monodromy groups 迭代单色群族的最大子群

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-04-17 DOI: 10.1017/s0017089524000120

Karthika Rajeev, Anitha Thillaisundaram

The Basilica group is a well-known 2-generated weakly branch, but not branch, group acting on the binary rooted tree. Recently, a more general form of the Basilica group has been investigated by Petschick and Rajeev, which is an

$s$

-generated weakly branch, but not branch, group that acts on the

$m$

-adic tree, for

$s,mge 2$

. A larger family of groups, which contains these generalised Basilica groups, is the family of iterated monodromy groups. With the new developments by Francoeur, the study of the existence of maximal subgroups of infinite index has been extended from branch groups to weakly branch groups. Here we show that a subfamily of iterated monodromy groups, which more closely resemble the generalised Basilica groups, have maximal subgroups only of finite index.

巴西利卡（Basilica）群是一个著名的作用于二叉有根树的 2 代弱分支但非分支群。最近，佩奇克（Petschick）和拉杰夫（Rajeev）研究了巴西利卡群的一种更一般的形式，即作用于 $m$ 有根树上的 $s$ 弱分支但无分支群，对于 $s,mge 2$ 而言。包含这些广义巴西利卡群的一个更大的群族是迭代单色群族。随着弗朗科尔的新发展，对无限指数最大子群存在性的研究已从分支群扩展到弱分支群。在这里，我们证明了迭代单色群的一个亚族，它更接近于广义巴西利卡群，但只有有限指数的最大子群。

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引用次数: 0

Twisted Blanchfield pairings and twisted signatures III: Applications 扭曲布兰奇菲尔德配对和扭曲签名 III：应用

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-04-15 DOI: 10.1017/s0017089524000077

Maciej Borodzik, Anthony Conway, Wojciech Politarczyk

This paper describes how to compute algorithmically certain twisted signature invariants of a knot

$K$

using twisted Blanchfield forms. An illustration of the algorithm is implemented on

$(2,q)$

-torus knots. Additionally, using satellite formulas for these invariants, we also show how to obstruct the sliceness of certain iterated torus knots.

本文介绍了如何利用扭曲布兰奇菲尔德形式从算法上计算一个结 $K$ 的某些扭曲签名不变式。该算法在$(2,q)$-torus结上实现。此外，利用这些不变式的卫星公式，我们还展示了如何阻碍某些迭代环结的切分性。

引用次数: 0

A note on quantum K-theory of root constructions 关于根构造的量子 K 理论的说明

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-04-12 DOI: 10.1017/s0017089524000089

Hsian-Hua Tseng

We consider K-theoretic Gromov-Witten theory of root constructions. We calculate some genus

$0$

K-theoretic Gromov-Witten invariants of a root gerbe. We also obtain a K-theoretic relative/orbifold correspondence in genus

$0$

我们考虑根构造的 K 理论 Gromov-Witten 理论。我们计算了一些0元属根球的K理论格罗莫夫-维滕不变式。我们还得到了 K 理论中 0$ 属的相对/双折叠对应关系。

引用次数: 0

On almost quotient Yamabe solitons 论几乎商的山边孤子

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-04-11 DOI: 10.1017/s0017089524000119

Willian Tokura, Marcelo Barboza, Elismar Batista, Priscila Kai

In this paper, we investigate the structure of certain solutions of the fully nonlinear Yamabe flow, which we call almost quotient Yamabe solitons as they extend quite naturally those already called quotient Yamabe solitons. We present sufficient conditions for a compact almost quotient Yamabe soliton to be either trivial or isometric with an Euclidean sphere. We also characterize noncompact almost gradient quotient Yamabe solitons satisfying certain conditions on both its Ricci tensor and potential function.

在本文中，我们研究了全非线性山边流的某些解的结构，我们称之为几乎商山边孤子，因为它们很自然地扩展了那些已经被称为商山边孤子的解。我们提出了紧凑型近商山边孤子与欧几里得球琐碎或等距的充分条件。我们还描述了在里奇张量和势函数上满足某些条件的非紧凑几乎梯度商山边孤子的特征。

引用次数: 0

Galois points and Cremona transformations 伽罗瓦点和克雷莫纳变换

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-04-11 DOI: 10.1017/s0017089524000090

Ahmed Abouelsaad

In this article, we study Galois points of plane curves and the extension of the corresponding Galois group to

$mathrm{Bir}(mathbb{P}^2)$

. We prove that if the Galois group has order at most

$3$

, it always extends to a subgroup of the Jonquières group associated with the point

$P$

. Conversely, with a degree of at least

$4$

, we prove that it is false. We provide an example of a Galois extension whose Galois group is extendable to Cremona transformations but not to a group of de Jonquières maps with respect to

$P$

. In addition, we also give an example of a Galois extension whose Galois group cannot be extended to Cremona transformations.

本文研究平面曲线的伽罗瓦点以及相应伽罗瓦群向 $mathrm{Bir}(mathbb{P}^2)$ 的扩展。我们证明，如果伽罗瓦群的阶最多为 $3$，那么它总是扩展到与点 $P$ 相关联的琼基耶斯群的一个子群。反之，如果阶数至少为 $4$，我们证明它是假的。我们提供了一个伽罗瓦扩展的例子，它的伽罗瓦群可以扩展到克雷莫纳变换，但不能扩展到关于 $P$ 的琼基耶尔映射群。此外，我们还给出了一个伽罗瓦扩展的例子，其伽罗瓦群不能扩展到克雷莫纳变换。

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引用次数: 0

Triangular matrix categories over quasi-hereditary categories 准遗传范畴上的三角矩阵范畴

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-03-21 DOI: 10.1017/s0017089524000053

Rafael Francisco Ochoa De La Cruz, Martin Ortíz Morales, Valente Santiago Vargas

In this paper, we prove that the lower triangular matrix category

$Lambda =left [ begin{smallmatrix} mathcal{T}&0 M&mathcal{U} end{smallmatrix} right ]$

, where

$mathcal{T}$

and

$mathcal{U}$

are

$textrm{Hom}$

-finite, Krull–Schmidt

$K$

-quasi-hereditary categories and

$M$

is an

$mathcal{U}otimes _K mathcal{T}^{op}$

-module that satisfies suitable conditions, is quasi-hereditary. This result generalizes the work of B. Zhu in his study on triangular matrix algebras over quasi-hereditary algebras. Moreover, we obtain a characterization of the category of the

$_Lambda Delta$

-filtered

$Lambda$

-modules.

在本文中，我们证明了下三角矩阵范畴 $Lambda =left [ begin{smallmatrix}mathcal{T}&0 M&mathcal{U}end{smallmatrix}其中 $mathcal{T}$ 和 $mathcal{U}$ 是$textrm{Hom}$ 无限的、Krull-Schmidt $K$ 准遗传范畴，而 $M$ 是满足适当条件的 $mathcal{U}otimes _K mathcal{T}^{op}$ 模块。这一结果概括了 B. Zhu 对准遗传代数上的三角形矩阵代数的研究。此外，我们还得到了$_Lambda Delta$ -过滤的$Lambda$ -模组范畴的特征。

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引用次数: 0

Models and integral differentials of hyperelliptic curves 超椭圆曲线的模型和积分微分

IF 0.5 4区数学 Q3 MATHEMATICS

Glasgow Mathematical Journal

Pub Date : 2024-03-18 DOI: 10.1017/s001708952400003x

Simone Muselli

Let $C; : ;y^2=f(x)$ be a hyperelliptic curve of genus $ggeq 1$ , defined over a complete discretely valued field $K$ , with ring of integers $O_K$ . Under certain conditions on $C$ , mild when residue characteristic is not $2$ , we explicitly construct the minimal regular model with normal crossings $mathcal{C}/O_K$ of $C$ . In the same setting we determine a basis of integral differentials of $C$ , that is an $O_K$ -basis for the global sections of the relative dualising sheaf <

让 $C; ：y^2=f(x)$是一条属$ggeq 1$的超椭圆曲线，定义在一个完整的离散值域$K$上，其整数环为$O_K$。在 $C$ 的某些条件下 , 当残差特征不为 2$ 时 , 我们明确地构造了具有法线交叉 $mathcal{C}/O_K$ 的最小正则模型 .在同样的背景下，我们确定了$C$的积分微分基础，即相对对偶化剪$omega _{mathcal{C}/O_K}$的全局截面的$O_K$基础。

引用次数: 0

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