Two filtrations of ribbon 2-knots

被引：17
|
作者：
Kanenobu, T [1 ]
Shima, A
机构：
[1] Osaka City Univ, Dept Math, Osaka 5588585, Japan
[2] Tokai Univ, Dept Math, Kanagawa 2591207, Japan
来源：
TOPOLOGY AND ITS APPLICATIONS | 2002年 / 121卷 / 1-2期
基金：
日本学术振兴会;
关键词：
finite type invariants; ribbon; 2-knots; filtrations;
D O I：
10.1016/S0166-8641(01)00115-8
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We have constructed a 'Vassiliev-like' filtration on the free abelian group generated by the set of ribbon 2-knots in 4-space in two ways: one is from a ribbon 2-disk, and the other from a projection of a ribbon 2-knot onto a generic 3-space whose singular set consists of only double points. Each filtration determines a notion of finite type invariants for ribbon 2-knots. We prove that the two filtrations are the same, and thus, the two finite type invariants are coincident. (C) 2002 Elsevier Science B.V. All rights reserved.
引用
收藏
页码：143 / 168
页数：26
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