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

Conference paper
Part of the Mathematics and Visualization book series (MATHVISUAL)

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.

Keywords

Fundamental Group Protein Backbone Geometric Graph Isotopy Class Cubical Complex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgements

This work was done during the EPSRC-funded secondment at Microsoft Research Cambridge, UK. We thank all reviewers for valuable comments and helpful suggestions.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of LiverpoolLiverpoolUK

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