The doodle of a finitely determined map germ from R 2 to R 3

Let f : U ⊂ R 2 → R 3 be a representative of a finitely determined map germ f : ( R 2 , 0 ) → ( R 3 , 0 ) . Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere S ϵ 2 centered at the origin in R 3 , call this curve the associated doodle of th...

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2009-07, Vol.221 (4), p.1281-1301
Main Authors: Marar, W.L., Nuño-Ballesteros, J.J.
Format: Article
Language:English
Subjects:
Doodle
Double point curve
Topological classification
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Summary:Let f : U ⊂ R 2 → R 3 be a representative of a finitely determined map germ f : ( R 2 , 0 ) → ( R 3 , 0 ) . Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere S ϵ 2 centered at the origin in R 3 , call this curve the associated doodle of the map germ f. For a large class of map germs the associated doodle has many transversal self-intersections. The topological classification of such map germs is considered from the point of view of the associated doodles.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2009.02.008