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

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

doi:10.1007/978-3-319-44684-4_21

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

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

Authors

Vitaliy Kurlin

H. Carr

C. Garth

T. Weinkauf

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. (2017). Computing invariants of knotted graphs given by sequences of points in 3-dimensional space. In Topological methods in data analysis and visualization IV : theory, algorithms, and applications (349-363). https://doi.org/10.1007/978-3-319-44684-4_21

Conference Name	Topology-Based Methods in Visualization 2015.
Conference Location	Annweiler, Germany
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