Three-page encoding and complexity theory for spatial graphs

Kurlin, V

doi:10.1142/s021821650700521x

Three-page encoding and complexity theory for spatial graphs

Kurlin, V

Authors

V Kurlin

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.