Groups with exotic finiteness properties from complex Morse theory

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Topology Pub Date : 2025-02-28 DOI:10.1112/topo.70013

Claudio Llosa Isenrich, Pierre Py

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引用次数: 0

Abstract

Recent constructions have shown that interesting behaviours can be observed in the finiteness properties of Kähler groups and their subgroups. In this work, we push this further and exhibit, for each integer $k$ , new hyperbolic groups admitting surjective homomorphisms to $Z$ and to $Z^{2}$ , whose kernel is of type $F_{k}$ but not of type $F_{k + 1}$ . By a fibre product construction, we also find examples of non-normal subgroups of Kähler groups with exotic finiteness properties.

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复莫尔斯理论中奇异有限性质群

最近的构造表明，在Kähler群及其子群的有限性质中可以观察到有趣的行为。在这项工作中，我们进一步推广了这一理论，并证明了对于每一个整数k$ k$，承认Z ${\mathbb {Z}}$和z2 ${\mathbb {Z}}^{2}$满同态的新双曲群。其内核类型为F k $\mathcal {F}_{k}$，但类型不为F k+1 $\mathcal {F}_{k+1}$。通过纤维积构造，我们还发现了具有奇异有限性质的Kähler群的非正规子群的例子。

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

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.