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Dissecting the 2-sphere by immersions

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Abstract

The self intersection of an immersion \(i: S^2 \to \mathbb {R}^3\) dissects S 2 into pieces which are planar surfaces (unless i is an embedding). In this work we determine what collections of planar surfaces may be obtained in this way. In particular, for every n we construct an immersion \(i: S^2 \to \mathbb {R}^3\) with 2n triple points, for which all pieces are discs.

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  1. Department of Mathematics, Bar-Ilan University, Ramat-Gan, 52900, Israel

    Tahl Nowik

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  1. Tahl Nowik
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Correspondence to Tahl Nowik.

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Nowik, T. Dissecting the 2-sphere by immersions. Geom Dedicata 127, 37–41 (2007). https://doi.org/10.1007/s10711-007-9153-9

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  • DOI: https://doi.org/10.1007/s10711-007-9153-9

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