Basic nets in the projective plane
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2013
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915046026641408 |
|---|---|
| author | Orevkov, S. Yu. |
| author_facet | Orevkov, S. Yu. |
| contents | 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). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1307_7377 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Basic nets in the projective plane Orevkov, S. Yu. Combinatorics 05C10 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). |
| title | Basic nets in the projective plane |
| topic | Combinatorics 05C10 |
| url | https://arxiv.org/abs/1307.7377 |