Topological invariants of stable maps of oriented 3-manifolds in 
                $$\mathbb {R}^4$$
                
                    
                        
                            
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Casonatto, C.; Fuster, María del Carmen Romero; Atique, R. Wik

doi:10.1007/s10711-017-0272-7

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Map Germs Of Fold Type1

Introduction1

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2020

2022

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Cited by 2 publications

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“…Combining lemmas 3.1 and 3.2 we can state the main result of this section. 4 , 0) be a map germ with Thom-Boardman type Σ 1,0 . Then, f is A-equivalent to a map germ of the form (x, y, z 2 , zp(x, y, z 2 )), where p ∈ m 3 .…”

Section: Map Germs Of Fold Typementioning

confidence: 99%

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The dual tree of a fold map germ from to

Pérez¹,

Nuño–Ballesteros²

2022

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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Let $f\colon (\mathbb {R}^{3},0)\to (\mathbb {R}^{4},0)$ 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 $S^{3}_\epsilon$ centred at the origin in $\mathbb {R}^{4}$ . 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.

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Section: Map Germs Of Fold Typementioning

confidence: 99%

“…If we centre our attention in recent results for map germs f : (R 3 , 0) → (R 4 , 0), Casonatto, Romero Fuster and Wik Atique have obtained in [4,5] Vassiliev invariants for stable maps of oriented 3-manifolds in R 4 . In the complex case, Houston and Kirk study in [7] the corank 1 A-classification.…”

Section: Introductionmentioning

confidence: 99%