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arXiv · 1307.7377

Basic nets in the projective plane

S. Yu. Orevkov
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Abstract

The notion of basic net (called also basic polyhedron) on $S^2$ plays a central role in Conway's approach to enumeration of knots and links in $S^3$. Drobotukhina applied this approach for links in $RP^3$ using basic nets on $RP^2$. By a result of Nakamoto, all basic nets on $S^2$ can be obtained from a very explicit family of minimal basic nets (the nets $(2\times n)^*$, $n\ge3$, in Conway's notation) by two local transformations. We prove a similar result for basic nets in $RP^2$. We prove also that a graph on $RP^2$ is uniquely determined by its pull-back on $S^3$ (the proof is based on Lefschetz fix point theorem).

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BibTeXRIS

S. Yu. Orevkov. 2014-09-16. Basic nets in the projective plane. https://doi.org/10.5802/afst.1446

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