量子自同构群的剩余有限性和无穷性质

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-08-06 DOI:10.1016/j.topol.2025.109538

Manpreet Singh

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引用次数: 0

摘要

研究了量子自同构群的剩余有限性和无穷性质。证明了有限生成的剩余有限群的自同构群是剩余有限的。我们为更广泛的一种褐煤建立了一个类似的结果。作为一个应用，我们证明了3球上一连杆的基本角的自同构群是残有限的。进一步证明了n股上的焊接编织群是剩余有限的。我们给出了无限量子阱的拓扑表征。此外，对于有限生成的无限群，证明了它们的自同构群和内自同构群是无限的。

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Residual finiteness and profinite properties of automorphism groups of quandles

We explore residual finiteness and profinite properties of automorphism groups of quandles. We prove that the automorphism group of finitely generated residually finite quandles is residually finite. We establish a similar result for a broader class of quandles. As an application, we prove that the automorphism group of the fundamental quandle of a link in the 3-sphere is residually finite. Furthermore, we prove that the welded braid group on n strands is residually finite. We provide a topological characterization of profinite quandles. Moreover, for finitely generated profinite quandles, we prove that the automorphism groups and the inner automorphism groups are profinite.

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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.