The dual tree of a fold map germ from R3 to R4

被引：1

作者：

Moya-Perez, J. A. ^{[1
]}

Nuno-Ballesteros, J. J. ^{[1
,2
]}

机构：

[1] Univ Valencia, Dept Matemat, Campus Burjassot, Burjassot 46100, Spain

[2] Univ Fed Paraiba, Dept Matemat, BR-58051900 Joao Pessoa, Paraiba, Brazil

来源：

PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS | 2023年 / 153卷 / 03期

关键词：

Dual tree; topological classification; double point curve; TOPOLOGICAL INVARIANTS; ORIENTED; 3-MANIFOLDS; CLASSIFICATION; SURFACES;

D O I：

10.1017/prm.2022.27

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f : (R-3,0) -> (R-4,0) be an analytic map germ with isolated instability. Its link is a stable map which is obtained by taking the intersection of the image of f with a small enough sphere S-epsilon(3) centred at the origin in R-4. If f is of fold type, we define a tree, that we call dual tree, that contains all the topological information of the link and we prove that in this case it is a complete topological invariant. As an application we give a procedure to obtain normal forms for any topological class of fold type.

引用

页码：958 / 977

页数：20

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