The Reeb Graph of a Map Germ from R3 to R2 with Non Isolated Zeros
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Data
2018-06-01
Autores
Batista, Erica Boizan
Costa, João Carlos Ferreira [UNESP]
Nuño-Ballesteros, Juan J.
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Resumo
We consider the topological classification of finitely determined map germs [f] : (R3, 0) → (R2, 0) with f- 1(0) ≠ { 0 }. The case 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 Sδ1 centered at the origin. The link is a stable map γf: N→ S1, where N is diffeomorphic to a sphere S2 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 Σ 2 , 1.
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Classification, Link, Reeb graph, Topological equivalence
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Bulletin of the Brazilian Mathematical Society, v. 49, n. 2, p. 369-394, 2018.