卫星节和瑟斯顿规范的主干数

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-04-03 DOI:10.1016/j.topol.2025.109383

Zehan Pan

引用次数: 0

摘要

假设J∧R3是一个非平凡结，并假设k´S1×D2是一个卫星图案。设N为S1×D2中子午盘的同调类对k的广义Thurston范数。设K为图案为K -的J的卫星结。我们证明了K的主干数严格大于N倍J的主干数。

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The trunk number of satellite knots and Thurston norm

Assume

J \subset R^{3}

is a non-trivial knot, and assume

\hat{k} \subset S^{1} \times D^{2}

is a satellite pattern. Let N be the generalized Thurston norm of the homology class of the meridian disk in

S^{1} \times D^{2}

with respect to

\hat{k}

. Let K be the satellite knot of J with pattern

\hat{k}

. We show that the trunk number of K is strictly greater than N times the trunk number of J.

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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.