Classification of algebraic tangles

Bartosz Ambrozy Gren; Joanna Ida Sulkowska; Boštjan Gabrovšek

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arXiv · 2504.06901

Classification of algebraic tangles

Bartosz Ambrozy Gren·Joanna Ida Sulkowska·Boštjan Gabrovšek

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Abstract

We study algebraic tangles as fundamental components in knot theory, developing a systematic approach to classify and tabulate prime tangles using a novel canonical representation. The canonical representation enables us to distinguish mutant tangles, which fills the gaps in previous classifications. Moreover, we increase the classification of prime tangles up to 14 crossings and analyze tangle symmetry groups. We provide a database of our results: https://tangleinfo.cent.uw.edu.pl.

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BibTeX RIS

Bartosz Ambrozy Gren, Joanna Ida Sulkowska, Boštjan Gabrovšek. 2025-04-09. Classification of algebraic tangles. https://arxiv.org/abs/2504.06901

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