Metrically Un-knotted Corank 1 Singularities of Surfaces in \(\mathbb {R}^4\)


The paper is devoted to relations between topological and metric properties of germs of real surfaces, obtained by analytic maps from \(\mathbb {R}^2\) to \(\mathbb {R}^4.\) We show that for a big class of such surfaces, the normal embedding property implies the triviality of the knot, presenting the link of the surfaces. We also present some criteria of normal embedding in terms of the polar curves.

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We would like to thank Alexandre Fernandes, Vincent Grandjean, and Edson Sampaio for interesting discussions and important remarks.

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Correspondence to L. Birbrair.

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Birbrair, L., Mendes, R. & Nuño-Ballesteros, J.J. Metrically Un-knotted Corank 1 Singularities of Surfaces in \(\mathbb {R}^4\). J Geom Anal 28, 3708–3717 (2018).

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  • Normal embedding
  • Link
  • Isolated singularity

Mathematics Subject Classification

  • 14B05
  • 32S50
  • 58K15