Three-page encoding and complexity theory for spatial graphs

Kurlin, V

Abstract

A finitely presented semigroup RSGn is constructed for n ≥ 2. The centre of RSGn encodes uniquely up to rigid ambient isotopy in 3-space all nonoriented spatial graphs with vertices of degree ≤ n. This encoding is obtained by using three-page embeddings of graphs into the three-page book T × I, where T is the cone on three points, and I is the unit segment. The notion of the three-page complexity for spatial graphs is introduced via three-page embeddings. This complexity satisfies the properties of finiteness and additivity under natural operations.

Citation

Kurlin, V. (2007). Three-page encoding and complexity theory for spatial graphs. Journal of Knot Theory and Its Ramifications, 16(01), 59-102. https://doi.org/10.1142/s021821650700521x

• Journal Article Type: Article
• Publication Date: Jan 1, 2007
• Deposit Date: Sep 21, 2007
• Journal: Journal of Knot Theory and Its Ramifications
• Print ISSN: 0218-2165
• Electronic ISSN: 1793-6527
• Publisher: World Scientific Publishing
• Peer Reviewed: Peer Reviewed
• Volume: 16
• Issue: 01
• Pages: 59-102
• DOI: https://doi.org/10.1142/s021821650700521x
• Keywords: Spatial graph, Ambient isotopy, Isotopy classification, Universal semigroup, Spatial graph, Ambient isotopy, Isotopy classification, Universal semigroup, Three-page embedding.
• Public URL: https://durham-repository.worktribe.com/output/1536360