Generic immersions of the two-sphere to $\mathbf R^3$ and their skeleta
Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 300-313
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Let $f\colon S^2\looparrowright\mathbb R^3$ be a generic smooth immersion. The skeleton of $f$ is the following triple $(\Gamma, D, p)$. $\Gamma$ is the 1-polyhedron of singular points of $f$, $D=f^{-1}(\Gamma)$ is also a 1-polyhedron, and $p\colon D\to\Gamma$, $x\mapsto f(x)$, is the projection. For triples of the form $(D,\Gamma, p)$, where $\Gamma$ has at most 4 vertices, we give an iff-condition under which the triple is the skeleton of a smooth immersion $f\colon S^2\looparrowright\mathbb R^3$.
@article{ZNSL_2003_299_a20,
author = {M. A. Stepanova},
title = {Generic immersions of the two-sphere to $\mathbf R^3$ and their skeleta},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {300--313},
year = {2003},
volume = {299},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a20/}
}
M. A. Stepanova. Generic immersions of the two-sphere to $\mathbf R^3$ and their skeleta. Zapiski Nauchnykh Seminarov POMI, Geometry and topology. Part 8, Tome 299 (2003), pp. 300-313. http://geodesic.mathdoc.fr/item/ZNSL_2003_299_a20/
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