Directional Invariants of Doubly Periodic Tangles-Reference-Cited by-同舟云学术

Directional Invariants of Doubly Periodic Tangles

Published:2024-07-30 Issue:8 Volume:16 Page:968
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Diamantis Ioannis¹^ORCID,Lambropoulou Sofia²^ORCID,Mahmoudi Sonia³⁴^ORCID

Affiliation:

1. Department of Data Analytics and Digitalisation, School of Business and Economics, Maastricht University, P.O. Box 616, 6200 MD Maastricht, The Netherlands

2. School of Applied Mathematical and Physical Sciences, Zografou Campus, National Technical University of Athens, GR-15780 Athens, Greece

3. Advanced Institute for Materials Research, Tohoku University, 2-1-1 Katahira, Aoba-ku, Sendai 980-8577, Japan

4. RIKEN iTHEMS Wako, Saitama 351-0198, Japan

Abstract

In this paper, we define novel topological invariants of doubly periodic tangles (DP tangles). DP tangles are embeddings of curves in the thickened plane with translational symmetries in two independent directions. We first organize the components of a DP tangle into different interlinked compounds, which are invariants of a DP tangle. The notion of an interlinked compound leads to the classification of DP tangles according to their directional type. We then prove that the directional type is an invariant of DP tangles using the concept of axis-motif, which can be viewed as the blueprint of a DP tangle.

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/8/968/pdf

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