JournalsrmiVol. 31, No. 3pp. 977–988

Gauss words and the topology of map germs from R3\mathbb R^3 to R3\mathbb R^3

  • Juan Antonio Moya-Pérez

    Universitat de València, Burjassot (Valencia), Spain
  • Juan José Nuño Ballesteros

    Universitat de València, Burjassot (Valencia), Spain
Gauss words and the topology of map germs from $\mathbb R^3$ to $\mathbb R^3$ cover
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Abstract

The link of a real analytic map germ f ⁣:(R3,0)(R3,0)f\colon (\mathbb{R}^{3}, 0) \to (\mathbb{R}^{3}, 0) is obtained by taking the intersection of the image with a small enough sphere Sϵ2S^2_\epsilon centered at the origin in R3\mathbb R^3. If ff is finitely determined, then the link is a stable map γ\gamma from S2S^2 to S2S^2. We define Gauss words which contains all the topological information of the link in the case that the singular set S(γ)S(\gamma) is connected and we prove that in this case they provide us with a complete topological invariant.

Cite this article

Juan Antonio Moya-Pérez, Juan José Nuño Ballesteros, Gauss words and the topology of map germs from R3\mathbb R^3 to R3\mathbb R^3. Rev. Mat. Iberoam. 31 (2015), no. 3, pp. 977–988

DOI 10.4171/RMI/860