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Dissecting the 2-sphere by immersions

Tahl Nowik
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Abstract

The self intersection of an immersion i : S^2 \to 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 R^3 with 2n triple points, for which all pieces are discs.

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Tahl Nowik. 2006-12-27. Dissecting the 2-sphere by immersions. https://arxiv.org/abs/math/0612796

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