Thompson群的稳定子群的Alexander定理

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-09-09 DOI:10.1016/j.topol.2025.109576

Yuya Kodama , Akihiro Takano

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引用次数: 0

摘要

2017年，Jones研究了Thompson群F的酉表示，并定义了一种从F构造结和链接的方法。他的一个结果是，任何结或链接都可以从这个群的一个元素中得到，这被称为亚历山大定理。另一方面，尽管汤普森群F有许多子群，但其中只有少数已知满足或不满足亚历山大定理。本文证明了在单位区间上的自然作用下，几乎所有的稳定子群都满足亚历山大定理。

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Alexander's theorem for stabilizer subgroups of Thompson's group

In 2017, Jones studied the unitary representations of Thompson's group F and defined a method to construct knots and links from F. One of his results is that any knot or link can be obtained from an element of this group, which is called Alexander's theorem. On the other hand, even though Thompson's group F has many subgroups, only a few of them are known to satisfy or not satisfy Alexander's theorem. In this paper, we prove that almost all stabilizer subgroups under the natural action on the unit interval satisfy Alexander's theorem.

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来源期刊

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.