Kurlin, V. (2007) 'Three-page encoding and complexity theory for spatial graphs.', Journal of knot theory and its ramifications., 16 (1). pp. 59-102.
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.
|Keywords:||Spatial graph, Ambient isotopy, Isotopy classification, Universal semigroup, Spatial graph, Ambient isotopy, Isotopy classification, Universal semigroup, Three-page embedding.|
|Full text:||Full text not available from this repository.|
|Publisher Web site:||http://dx.doi.org/10.1142/S021821650700521X|
|Record Created:||21 Sep 2007|
|Last Modified:||08 Apr 2009 16:36|
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