Search results for "topological classification"

Topological classification of gradient-like diffeomorphisms on 3-manifolds

2004

Abstract We give a complete invariant, called global scheme , of topological conjugacy classes of gradient-like diffeomorphisms, on compact 3-manifolds. Conversely, we can realize any abstract global scheme by such a diffeomorphism.

The doodle of a finitely determined map germ from R2 to R3

AbstractLet f:U⊂R2→R3 be a representative of a finitely determined map germ f:(R2,0)→(R3,0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere Sϵ2 centered at the origin in R3, 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.

The doodle of a finitely determined map germ from R2 to R3

2009

Let f:U⊂R2→R3 be a representative of a finitely determined map germ f:(R2,0)→(R3,0). Consider the curve obtained as the intersection of the image of the mapping f with a sufficiently small sphere Sϵ2 centered at the origin in R3, 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.

Finitely determined singularities of ruled surfaces in 3

2009

AbstractWe study local singularities of ruled surfaces in 3. We show that any map germ f : (2, 0) → (3, 0) with a simple singularity is -equivalent to a ruled surface. Moreover, we give a topological classification of -finitely determined singularities of ruled surfaces and show that there are just eleven topological classes.

Double points in families of map germs from ℝ2 to ℝ3

2020

We show that a 1-parameter family of real analytic map germs [Formula: see text] with isolated instability is topologically trivial if it is excellent and the family of double point curves [Formula: see text] in [Formula: see text] is topologically trivial. In particular, we deduce that [Formula: see text] is topologically trivial when the Milnor number [Formula: see text] is constant.

Gauss words and the topology of finitely determined map germs from R^n to R^n

2013

El objetivo de este trabajo es la clasificación topológica de gérmenes de aplicación finitamente determinados en el caso real equidimensional, es decir, de R^n en R^n, mediante la construcción de un invariante topológico completo asociado al link de dichos gérmenes. El link se define como la intersección de la imagen de un representante de nuestro germen f con una esfera S^n centrada en el origen y suficientemente pequeña. Para el caso n=2, una vez construido dicho invariante (las palabras de Gauss adaptadas a este caso particular), obtenemos la clasificación topológica de dichos gérmenes prácticamente en su totalidad en el caso de corrango 1 y parcialmente en el caso de corrango 2. Por últ…

The link of a finitely determined map germ from R 2 to R 2

2010

Let f: (R2, 0) → (R2, 0) be a finitely determined map germ. The link of f is obtained by taking a small enough representative f: U ⊂ R2 → R2 and the intersection of its image with a small enough sphere Sε1 centered at the origin in R2. We will describe the topology of f in terms of the Gauss word associated to its link.