Simplicial volume of manifolds with amenable fundamental group at infinity

IF 0.5 4区数学 Q3 MATHEMATICS Glasgow Mathematical Journal Pub Date : 2024-04-22 DOI:10.1017/s0017089524000107

Giuseppe Bargagnati

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引用次数: 0

Abstract

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.

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流形的简单体积，其基本群在无穷远处是可调和的

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Glasgow Mathematical Journal 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Glasgow Mathematical Journal publishes original research papers in any branch of pure and applied mathematics. An international journal, its policy is to feature a wide variety of research areas, which in recent issues have included ring theory, group theory, functional analysis, combinatorics, differential equations, differential geometry, number theory, algebraic topology, and the application of such methods in applied mathematics. The journal has a web-based submission system for articles. For details of how to to upload your paper see GMJ - Online Submission Guidelines or go directly to the submission site.

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