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JA Moya-Pérez, JJ Nuño-Ballesteros (2014)
Topological classification of corank 1 map germs from $${\mathbb{R}}^3$$ R 3 to $${\mathbb{R}}^3$$ R 3Rev. Mat. Complut., 27
J. Moya-Pérez, J. Nuño-Ballesteros (2010)
The link of a finitely determined map germ from R2 to R2Journal of The Mathematical Society of Japan, 62
(1946)
Sur les points singuliers d ’ une forme de Pfaff completement intégrable ou d ’ une fonction numérique
J. Moya-Pérez, J. Ballesteros (2015)
Gauss words and the topology of map germs from $\mathbb R^3$ to $\mathbb R^3$Revista Matematica Iberoamericana, 31
V. Arnold (2007)
Topological Classification of Morse Functions and Generalisations of Hilbert’s 16-th ProblemMathematical Physics, Analysis and Geometry, 10
V. Arnold (2009)
Topological Classification of Morse Functions and Generalisations of Hilbert's 16-th ProblemTopologica, 2
V. Sharko (2003)
Smooth and Topological Equivalence of Functions on SurfacesUkrainian Mathematical Journal, 55
EB Batista, JCF Costa, JJ Nuño-Ballesteros (2017)
The Reeb graph of a map germ from $${\mathbb{R}}^3$$ R 3 to $${\mathbb{R}}^2$$ R 2 with isolated zerosProc. Edinb. Math. Soc., 60
(2016)
The generalized Reeb graph of stable functions
JA Moya-Pérez, JJ Nuño-Ballesteros (2010)
The link of finitely determined map germ from $${\mathbb{R}}^2$$ R 2 to $${\mathbb{R}}^2$$ R 2J. Math. Soc. Jpn., 62
A. Varčenko (1974)
LOCAL TOPOLOGICAL PROPERTIES OF DIFFERENTIABLE MAPPINGSMathematics of The Ussr-izvestiya, 8
A. Prishlyak (1999)
Topological equivalence of smooth functions with isolated critical points on a closed surfaceTopology and its Applications, 119
(2015)
Sobre a classificação topológica de germes finitamente determinados de R 3 em R 2
A. J., J. J. (2010)
The link of a finitely determined map germ from R 2 to R 2
J. Moya-Pérez, J. Nuño-Ballesteros (2014)
Topological classification of corank 1 map germs from R 3 to R 3
T. Fukuda (1985)
Local Topological Properties of Differentiable Mappings IITokyo Journal of Mathematics, 08
J. Costa, J. Nuno-Ballesteros (2013)
Topological $${\mathcal{K}}$$ -classification of finitely determined map germsGeometriae Dedicata, 166
(2017)
The cone structure theorem for map-germs with non isolated zeros
JA Moya-Pérez, JJ Nuño-Ballesteros (2015)
Gauss words and the topology of map germs from $${\mathbb{R}}^3$$ R 3 to $${\mathbb{R}}^3$$ R 3Rev. Mat. Iberoam., 31
J. Moya-Pérez, J. Nuño-Ballesteros (2014)
Topological classification of corank 1 map germs from $$\mathbb {R}^{3}$$R3 to $$\mathbb {R}^{3}$$R3Revista Matemática Complutense, 27
E. Batista, J. Costa, J. Nuño-Ballesteros (2017)
THE REEB GRAPH OF A MAP GERM FROM R3 TO R2 WITH ISOLATED ZEROS
C. Wall (1981)
Finite Determinacy of Smooth Map‐GermsBulletin of The London Mathematical Society, 13
JCF Costa, JJ Nuño-Ballesteros (2013)
Topological $$\cal{K}$$ K -classification of finitely determined map germsGeom. Dedicata, 166
We consider the topological classification of finitely determined map germs $$[f]:(\mathbb {R}^3,0)\rightarrow (\mathbb {R}^2,0)$$ [ f ] : ( R 3 , 0 ) → ( R 2 , 0 ) with $$f^{-1}(0)\ne \{0\}$$ f - 1 ( 0 ) ≠ { 0 } . The case $$f^{-1}(0) = \{0\}$$ f - 1 ( 0 ) = { 0 } was treated in another recent paper by the authors. The main tool used to describe the topological type is the link of [f], which is obtained by taking the intersection of its image with a small sphere $$S^1_\delta $$ S δ 1 centered at the origin. The link is a stable map $$\gamma _f:N\rightarrow S^1$$ γ f : N → S 1 , where N is diffeomorphic to a sphere $$S^2$$ S 2 minus 2L disks. We define a complete topological invariant called the generalized Reeb graph. Finally, we apply our results to give a topological description of some map germs with Boardman symbol $$\Sigma ^{2,1}$$ Σ 2 , 1 .
Bulletin of the Brazilian Mathematical Society, New Series – Springer Journals
Published: Nov 16, 2017
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