加厚曲面中连杆的端基本跨越曲面

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2024-12-27 DOI:10.1016/j.topol.2024.109187

Thomas Kindred

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引用次数: 0

摘要

设D为闭合可定向曲面Σ上的元胞交替连杆图。我们证明如果D没有可移动的核交叉点，那么D的每个棋盘表面都是π -必要的，并且不包含在Σ×I中∂-平行的必要闭曲线。我们的主要动机来自于另一篇论文的技术方面，在这篇论文中，我们证明了Tait的飞行猜想适用于交替的虚拟链路。我们还描述了通过图拉耶夫表面的可能应用。

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End-essential spanning surfaces for links in thickened surfaces

Let D be a cellular alternating link diagram on a closed orientable surface Σ. We prove that if D has no removable nugatory crossings then each checkerboard surface from D is

π_{1}

-essential and contains no essential closed curve that is ∂-parallel in

Σ \times I

. Our chief motivation comes from technical aspects of a companion paper, where we prove that Tait's flyping conjecture holds for alternating virtual links. We also describe possible applications via Turaev surfaces.

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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.