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Three-page encoding and complexity theory for spatial graphs

V. Kurlin
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Abstract

We construct a series of finitely presented semigroups. The centers of these semigroups encode uniquely up to rigid ambient isotopy in 3-space all non-oriented spatial graphs. This encoding is obtained by using three-page embeddings of graphs into the product of the line with the cone on three points. By exploiting three-page embeddings we introduce the notion of the three-page complexity for spatial graphs. This complexity satisfies the properties of finiteness and additivity under natural operations.

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V. Kurlin. 2004-07-19. Three-page encoding and complexity theory for spatial graphs. https://arxiv.org/abs/math/0407321

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