ON THE TRANSIENT NUMBER OF A KNOT

被引：0

作者：

Eudave-Munoz, Mario ^{[1
]}

Aguilar, Joan Carlos Segura ^{[1
]}

机构：

[1] Univ Nacl Autonoma Mexico, Inst Matemat, Mexico City, Mexico

来源：

PACIFIC JOURNAL OF MATHEMATICS | 2024年 / 332卷 / 01期

关键词：

knot; transient number; unknotting number; tunnel number; double branched covers; UNKNOTTING NUMBER;

D O I：

10.2140/pjm.2024.332.69

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The transient number of a knot K, denoted tr(K), is the minimal number of simple arcs that have to be attached to K, in order for K to be homotoped to a trivial knot in a regular neighborhood of the union of K and the arcs. We give a lower bound for tr(K) in terms of the rank of the first homology group of the double branched cover of K. In particular, if tr(K) = 1, then the first homology group of the double branched cover of K is cyclic. Using this, we can calculate the transient number of many knots in the tables and show that there are knots with arbitrarily large transient number.

引用

页码：7 / 89

页数：24

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