连杆的本征对称群

IF 0.6 3区数学 Q3 MATHEMATICS

Algebraic and Geometric Topology Pub Date : 2021-10-07 DOI:10.2140/agt.2023.23.2347

C. Livingston

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引用次数: 0

摘要

对称群通过元素的置换作用于3球中有序n元链的同位素类集。连杆的本然对称群S(L)定义为对称群中保持L作为无取向连杆的有序同位素型的元素的集合。对这些群的研究始于1969年，但对称群的每一个子群是否都是某种联系的本然对称群的问题一直没有解决。我们提供反例;特别地，如果n>5，则不存在S(L)为交替群的n组分链路L。

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Intrinsic symmetry groups of links

The set of isotopy classes of ordered n-component links in the 3-sphere is acted on by the symmetric group via permutation of the components. The intrinsic symmetry group of the link, S(L), is defined to be the set of elements in the symmetric group that preserve the ordered isotopy type of L as an unoriented link. The study of these groups was initiated in 1969, but the question of whether or not every subgroup of the symmetric group arises as an intrinisic symmetry group of some link has remained open. We provide counterexamples; in particular, if n>5, then there does not exist an n-component link L for which S(L) is the alternating group.

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来源期刊

Algebraic and Geometric Topology 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

6-12 weeks

期刊介绍： Algebraic and Geometric Topology is a fully refereed journal covering all of topology, broadly understood.