The multi-region index of a knot

被引：0

作者：

Goodhill, Sarah ^{[1
]}

Lowrance, Adam M. ^{[1
]}

Gonzales, Valeria Munoz ^{[1
]}

Rattray, Jessica ^{[1
]}

Zeh, Amelia ^{[1
]}

机构：

[1] Vassar Coll, Dept Math & Stat, Poughkeepsie, NY 12601 USA

来源：

JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2020年 / 29卷 / 04期

关键词：

Knot; region crossing change; unknotting; unknotting number; region index;

D O I：

10.1142/S0218216520500224

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using region crossing changes, we define a new invariant called the multi-region index of a knot. We prove that the multi-region index of a knot is bounded from above by twice the crossing number of the knot. In addition, we show that the minimum number of generators of the first homology of the double branched cover of S-3 over the knot is strictly less than the multi-region index. Our proof of this lower bound uses Goeritz matrices.

引用

页数：16

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