SINGULARITY KNOTS OF MINIMAL SURFACES IN R4

被引：4
|
作者：
Soret, Marc [1 ]
Ville, Marina [2 ]
机构：
[1] Univ Tours, Dept Math, F-37000 Tours, France
[2] Univ Paris, Inst Math Jussieu, CNRS, UMR 7586, F-75205 Paris 13, France
来源：
JOURNAL OF KNOT THEORY AND ITS RAMIFICATIONS | 2011年 / 20卷 / 04期
关键词：
Minimal surfaces; knots; braids; branch points; harmonic; conformal; singularities;
D O I：
10.1142/S0218216511009406
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study knots in S-3 obtained by the intersection of a minimal surface in R-4 with a small 3-sphere centered at a branch point. We construct new examples of minimal knots. In particular we show the existence of non-fibered minimal knots. We show that simple minimal knots are either reversible or fully amphicheiral; this yields an obstruction for a given knot to be a simple minimal knot. Properties and invariants of these knots such as the algebraic crossing number of a braid representative and the Alexander polynomial are studied.
引用
收藏
页码：513 / 546
页数：34
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