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Over then under tangles.
- Source :
-
Journal of Knot Theory & Its Ramifications . Jun2023, Vol. 32 Issue 8, p1-40. 40p. - Publication Year :
- 2023
-
Abstract
- Over-then-Under (OU) tangles are oriented tangles whose strands travel through all of their over crossings before any under crossings. In this paper, we discuss the idea of gliding: an algorithm by which tangle diagrams could be brought to OU form. By analyzing cases in which the algorithm converges, we obtain a braid classification result, which we also extend to virtual braids, and provide a Mathematica implementation. We discuss other instances of successful "gliding ideas" in the literature — sometimes in disguise — such as the Drinfel'd double construction, Enriquez's work on quantization of Lie bialgebras, and Audoux and Meilhan's classification of welded homotopy links. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGORITHMS
*CLASSIFICATION
Subjects
Details
- Language :
- English
- ISSN :
- 02182165
- Volume :
- 32
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Knot Theory & Its Ramifications
- Publication Type :
- Academic Journal
- Accession number :
- 171844977
- Full Text :
- https://doi.org/10.1142/S0218216523400035