Dissecting the 2-sphere by immersions

Details Dissecting the 2-sphere by immersions Dissecting the 2-sphere by immersions

2006-12-27

arxiv.org/abs/math/0612796v1

Mathematics

Geometric Topology

Scientific paper

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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