Computing invariants of knotted graphs given by sequences of points in 3-dimensional space

Kurlin, Vitaliy; Carr, H.; Garth, C.; Weinkauf, T.

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.

Citation

Kurlin, V., Carr, H., Garth, C., & Weinkauf, T. (2015, May). Computing invariants of knotted graphs given by sequences of points in 3-dimensional space. Presented at Topology-Based Methods in Visualization 2015., Annweiler, Germany

• Presentation Conference Type: Conference Paper (published)
• Conference Name: Topology-Based Methods in Visualization 2015.
• Start Date: May 20, 2015
• End Date: May 22, 2015
• Acceptance Date: Feb 20, 2015
• Online Publication Date: Jun 3, 2017
• Publication Date: Jun 3, 2017
• Deposit Date: May 11, 2015
• Pages: 349-363
• Series Title: Mathematics and visualization
• Series ISSN: 1612-3786
• Book Title: Topological methods in data analysis and visualization IV : theory, algorithms, and applications.
• ISBN: 9783319446820
• DOI: https://doi.org/10.1007/978-3-319-44684-4_21
• Public URL: https://durham-repository.worktribe.com/output/1152482