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.

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Keywords
ribbon graph, links in real projective space, Turaev surface, virtual link, partial dual, Tait graph
Mathematical Subject Classification 2010
Primary: 57M15
Secondary: 05C10
Milestones
Received: 28 August 2014
Revised: 6 February 2015
Accepted: 6 February 2015
Published: 17 December 2015

Communicated by Józef H. Przytycki
Authors
Iain Moffatt
Department of Mathematics
Royal Holloway University of London
Egham, Surrey
TW20 0EX
United Kingdom
Johanna Strömberg
Department of Mathematics
Royal Holloway University of London
Egham, Surrey
TW20 0EX
United Kingdom