Computing Invariants of Knotted Graphs Given by Sequences of Points in 3-Dimensional Space

Kurlin, Vitaliy ORCID: 0000-0001-5328-5351 (2017) Computing Invariants of Knotted Graphs Given by Sequences of Points in 3-Dimensional Space. In: Mathematics and Visualization. Mathematics and Visualization . Springer International Publishing, pp. 349-363. ISBN 9783319446820

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Abstract

We design a fast algorithm for computing the fundamental group of the complement to any knotted polygonal graph in 3-space. A polygonal graph consists of straight segments and is given by sequences of vertices along edge-paths. This polygonal model is motivated by protein backbones described in the Protein Data Bank by 3D positions of atoms. Our KGG algorithm simplifies a knotted graph and computes a short presentation of the Knotted Graph Group containing powerful invariants for classifying graphs up to isotopy. We use only a reduced plane diagram without building a large complex representing the complement of a graph in 3-space.

Item Type:	Book Section
Depositing User:	Symplectic Admin
Date Deposited:	03 Jul 2017 08:06
Last Modified:	14 Mar 2024 17:32
DOI:	10.1007/978-3-319-44684-4_21
Related URLs:	Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3008277