#### Vol. 9, No. 1, 2016

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On the ribbon graphs of links in real projective space

### Iain Moffatt and Johanna Strömberg

Vol. 9 (2016), No. 1, 133–153
##### Abstract

Every link diagram can be represented as a signed ribbon graph. However, different link diagrams can be represented by the same ribbon graphs. We determine how checkerboard colourable diagrams of links in real projective space, and virtual link diagrams, that are represented by the same ribbon graphs are related to each other. We also find moves that relate the diagrams of links in real projective space that give rise to (all-$A$) ribbon graphs with exactly one vertex.

##### Keywords
ribbon graph, links in real projective space, Turaev surface, virtual link, partial dual, Tait graph
Primary: 57M15
Secondary: 05C10